Question

If $\theta$ is a positive acute angle such that $sec\theta =cosec{60}^{\circ }$, find the value of $2co{s}^2\theta -1$.

Answer 1

=> $sec\theta =cosec{60}^{\circ }$

=> $\frac{1}{cos\theta }$ = $\frac{1}{sin60}$

=>$cos\theta$ = $sin60$

=> $cos\theta$= $\sqrt{\frac{3}{2}}$

=>$2co{s}^2\theta -1$ = $2(cos\theta {)}^2-1$

= 2$\times (\sqrt{\frac{3}{2}}{)}^2$ -1

= 2$\times (\frac{3}{4}$) - 1

= $\frac{3}{2}$ - 1

= $\frac{1}{2}$