If and , then the value of…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

x_k=(\sec\theta)^{\frac{1}{2^k}}+(\tan\theta)^{\frac{1}{2^k}}

and

y_k=(\sec\theta)^{\frac{1}{2^k}}-(\tan\theta)^{\frac{1}{2^k}}

, then the value of

3y_n\prod_{k=0}^{n}x_k