Example 16 - Chapter 3 Class 11 Trigonometric Functions

Last updated at April 16, 2024 by Teachoo

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Example 16 Prove that 𝑐𝑜𝑠⁡〖7𝑥 + 𝑐𝑜𝑠⁡5𝑥 〗/𝑠𝑖𝑛⁡〖7𝑥 − 𝑠𝑖𝑛⁡5𝑥 〗 = cot x Solving L.H.S. We solve cos 7x + cos 5x & sin 7x – sin 5x separately cos 7x + cos 5x = 2 cos ((𝟕𝒙 + 𝟓𝒙)/𝟐) cos ((𝟕𝒙 − 𝟓𝒙)/𝟐) = 2 cos (12𝑥/2) cos (2𝑥/2) = 2 cos 6x cos x sin 7x – sin 5x = 2 cos ((𝟕𝒙 + 𝟓𝒙)/𝟐) sin((𝟕𝒙 − 𝟓𝒙)/𝟐) = 2 cos (12𝑥/2) sin (2𝑥/2) = 2 cos 6x sin x Now 〖𝑐𝑜𝑠 〗⁡〖7𝑥 + 𝑐𝑜𝑠⁡5𝑥 〗/𝑠𝑖𝑛⁡〖7𝑥 − 𝑠𝑖𝑛⁡5𝑥 〗 = (𝟐 〖 𝒄𝒐𝒔 〗⁡〖𝟔𝒙 𝒄𝒐𝒔⁡𝒙 〗)/(𝟐 𝒄𝒐𝒔⁡〖 𝟔𝒙 𝒔𝒊𝒏⁡𝒙 〗 ) = 𝑐𝑜𝑠⁡〖 𝑥〗/𝑠𝑖𝑛⁡〖 𝑥〗 = cot x = R.H.S. Hence L.H.S. = R.H.S. Hence proved

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Davneet Singh

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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