<\/span><\/p>\n The value of tan (90\u00b0) is infinity (<\/span>\u221e)<\/span>\u00a0<\/b>or<\/span> not defined.<\/span><\/p>\n tan (90\u00b0) = tan \u03c0\/2 = <\/b>\u221e (not defined)<\/b><\/p>\n The exact value of tan \u03c0\/2 can be derived using a unit circle and by the trigonometric approach.<\/span><\/p>\n We can derive the value of tan (90\u00b0) by using a unit circle. The unit circle is a circle that has a radius equal to 1.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Because the radius is 1, we can easily measure the values of sin, cos and tan.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n The figure shown above is a graphical representation of sin, cos and tan values in a unit circle.\u00a0 When the angle is 0\u00b0, this will change the figure given below.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Now, let us see the condition when the angle is 90\u00b0<\/span><\/p>\n <\/span><\/p>\n From the above figure, it is clear that when the angle is 90\u00b0, we can not define the value of tan. Therefore, the value of tan (90\u00b0) is undefined.<\/span><\/p>\n <\/span><\/p>\n Alternate method:\u00a0<\/b><\/p>\n <\/b><\/p>\n <\/span><\/p>\n Since the angle is 90 degrees, there will not be any particular triangle but a unit circle. Any point at 90\u00b0 can be described as (0,y) because the value at X-axes will be zero.<\/span><\/p>\n Unit circle has a radius of 1 which means the height (y) is 1.\u00a0<\/span><\/p>\n Therefore, tan (90\u00b0) = y\/x<\/span><\/p>\n tan (90\u00b0) = 1\/0<\/span><\/p>\n It is undefined because you can’t divide any number by zero.<\/span><\/p>\n Hence tan (90\u00b0) = <\/span>\u221e or not defined.<\/span><\/p>\n <\/span><\/p>\n We can prove the value of tan (90\u00b0) with a trigonometric approach.<\/span><\/p>\n we know that sin 90\u00b0 = 1 and cos 90\u00b0 = 0<\/span><\/p>\n Also, by trigonometric identities,<\/span><\/p>\n sin x\/cos x = tan x<\/b><\/p>\n Put x = 90\u00b0<\/span><\/p>\n tan (90\u00b0) = sin (90\u00b0)\/cos (90\u00b0)<\/span><\/p>\n Put the values of sin 90\u00b0 and cos 90\u00b0<\/span><\/p>\n tan (90\u00b0) = 1\/0 which can not be defined.<\/span><\/p>\n <\/span><\/p>\n tan (90\u00b0 – \u03b8 ) = cot \u03b8<\/span><\/p>\n tan (90\u00b0 + \u03b8 ) = – cot \u03b8<\/span><\/p>\n tan (-\u03b8 )= – tan \u03b8<\/span><\/p>\n \\operatorname{Tan} 2 x=2 \\tan x \/\\left(1-\\tan ^{2} x\\right) <\/span> <\/p>\n <\/b><\/p>\n 1. Evaluate: tan (90 – 30)\u00b0<\/strong> Solution:<\/strong><\/p>\n We know that <\/span>tan (90\u00b0 – \u03b8 ) = cot \u03b8<\/span><\/p>\n So, tan (90 – 30)\u00b0 = cot 30\u00b0<\/span><\/p>\n and cot 30\u00b0 = <\/span>\u221a3<\/p>\n Therefore,<\/span> \u00a0tan (90 – 30)\u00b0 = <\/span>\u221a3<\/p>\n <\/b><\/p>\n 2. Evaluate 2 tan 135\u00b0 \u2013 2 sin 30\u00b0<\/strong><\/p>\n Solution:<\/strong> tan (135\u00b0) = tan (90 + 45)\u00b0<\/span><\/p>\n We know that <\/span>tan (90 + \u03b8) = -cot \u03b8<\/span><\/p>\n So, <\/span>tan (90 + 45)\u00b0 = -cot 45\u00b0 = -1<\/span><\/p>\n and sin 30\u00b0 = 1\/2<\/span><\/p>\n Substituting the values,\u00a0<\/span><\/p>\n 2 tan 135\u00b0 \u2013 2 sin 30\u00b0<\/span><\/p>\n = 2 (-1) – 2(\u00bd)<\/span><\/p>\n = -2 – 1<\/span><\/p>\n = -3<\/span>\u00a0<\/b><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\nValue of Tan 90\u00b0<\/b><\/h2>\n
<\/b><\/h2>\n
Proof<\/b><\/h2>\n
\n
Unit circle<\/b><\/h3>\n<\/li>\n<\/ul>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Tan-90-Degrees-01-300x252.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Tan-90-Degrees-02-300x230.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Tan-90-Degrees-03-300x229.png\")
<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Tan-90-Degrees-04-1-294x300.png\")
<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Tan-90-Degrees-05-300x252.png\")
<\/b><\/p>\n\n
Trigonometric Method<\/b><\/h3>\n<\/li>\n<\/ul>\n
Some Important Formulas<\/b><\/h2>\n
\\operatorname{Tan} 3 x=\\left(3 \\tan x-\\tan ^{3} x\\right) \/\\left\\{\\left(1-\\left(3 \\tan ^{2} x\\right)\\right\\}\\right.\n<\/span>
<\/span><\/p>\nExample<\/b><\/h2>\n
<\/b><\/p>\n
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\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n