Question

Evaluate: $\frac{cose{c}^2{63}^o+{\tan }^2{24}^o}{{\cot }^2{66}^o+{\sec }^2{27}^o}+\frac{{\sin }^2{63}^o+{\cos }^2{63}^o\sin {27}^o+\sin {27}^o\sec {63}^o}{2(co{\sec }^2{65}^o-{\tan }^2{25}^o)}$

Answer 1

$\frac{cose{c}^2{63}^o+{\tan }^2{24}^o}{{\cot }^2{66}^o+{\sec }^2{27}^o}+\frac{{\sin }^2{63}^o+{\cos }^2{63}^o\sin {27}^o+\sin {27}^o\sec {63}^o}{2(cose{c}^2{65}^o-{\tan }^2{25}^o)}$

$=\frac{{\sec }^2(90-{63}^o)+{\cot }^2(90-24)}{{\cot }^2{66}^o+{\sec }^{2}27}+$....

$=\frac{{\sec }^2{27}^o+{\cot }^2{66}^o}{{\cot }^2{66}^o+{\sec }^2{27}^o}+\frac{{\sin }^{2}63+\sin {27}^{o}cosec{27}^o+{\cos }^2{63}^o-\cos {63}^o}{2({\sec }^2{25}^o-{\tan }^{2}25)}$

$=1+\frac{1+{\sin }^2{63}^o+{\cos }^3{63}^o}{2}$.