Ex 3.3

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Chapter 3 Class 11 Trigonometric Functions

Serial order wise

Last updated at April 16, 2024 by Teachoo

Ex 3.3, 10 Prove that sinβ‘(π + 1)π₯ sinβ‘(π + 2)π₯+cosβ‘(π + 1)π₯ cosβ‘(π + 2)π₯=cosβ‘π₯ Solving L.H.S. We know that cos ( A β B) = cos A cos B + sin A sin B Here, A = (n + 1)x ,B = (n + 2)x Hence sinβ‘(π+1)π₯ sinβ‘(π+2)π₯+cosβ‘(π + 1)π₯ cosβ‘(π + 2)π₯ = cos [ (n + 1)x β (n + 2)x ] = cos [ nx + x β nx β 2x ] = cos [ nx β nx + x β 2 x ] = cos (0 β x ) = cos (β x) = cos x = R.H.S. Hence , L.H.S. = R.H.S. Hence proved