Question

Evaluate : [sec² (90° - $) - cot²$/2 (sin²25° + sin²65º)]+ [2 cos² 60°tan²28°-tan²62°/3 (sec²43° - cot² 47°)]​

Answer 1

(sec²(90°- θ) - cot²θ)/2(sin²25° + sin²65°) - (2 cos² 60° tan²28° tan²47°)/3(sec²43° - cot²47°

$\large \bold \red{ = \frac{( \cosec {}^{2} \theta - \cot {}^{2} \theta)}{2( \sin {}^{2}25 \degree + \cos {}^{2} 25 \degree)} }$

$\large \bold \red{= - \frac{2 \times \frac{1}{2} \times \frac{1}{2} { \tan}^{2}28 \degree \times \cot{}^{2}28 \degree }{3[ \sec {}^{2}43 \degree - \tan {}^{2} 43 \degree ]}}$

$\large \bold \red{= \frac{1}{2 \times (1)} - \frac{ \frac{1}{2} \times \tan^228 \degree \times \frac{1}{ \tan {}^{2} 28 \degree} }{3} }$

$= \frac{1}{2} - \frac{1}{6} = \frac{1}{3}$