Ex 3.3, 8 - Chapter 3 Class 11 Trigonometric Functions

Last updated at April 16, 2024 by Teachoo

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Ex 3.3, 8 Prove that cos⁡〖 (π + 𝑥) cos⁡〖(− 𝑥)〗〗/(sin⁡〖 (π − 𝑥)〗 cos⁡〖"(" π/2 " + " 𝑥")" 〗 ) = cot2 𝑥 Solving L.H.S. 𝒄𝒐𝒔⁡〖(𝝅 + 𝒙) 〖𝒄𝒐𝒔 〗⁡〖(−𝒙)〗〗/(𝒔𝒊𝒏⁡(𝝅 − 𝒙) 𝒄𝒐𝒔⁡〖"(" 𝝅/𝟐 " + " 𝒙")" 〗 ) Putting π = 180° = 𝑐𝑜𝑠⁡〖(180° + 𝑥) 〖𝑐𝑜𝑠 〗⁡〖(−𝑥)〗〗/(𝑠𝑖𝑛⁡(180° − 𝑥) 𝑐𝑜𝑠⁡〖"(" 90° "+ " 𝑥")" 〗 ) Using cos (180° + x) = –cos x cos (−x) = cos x sin (180° – x) = sin x & cos(90° + x) = –sin x = (−𝒄𝒐𝒔⁡〖𝒙 × 𝒄𝒐𝒔⁡𝒙 〗)/((𝒔𝒊𝒏⁡〖𝒙) ×〖(−𝒔𝒊𝒏〗⁡𝒙) 〗 ) = (−𝑐𝑜𝑠2𝑥)/(−𝑠𝑖𝑛2𝑥) = cot2x = R.H.S. Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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