Ex 3.3, 10 - Chapter 3 Class 11 Trigonometric Functions

Transcript

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