Question

Evaluate: $\frac{{\sec 29}^{\circ }}{\text{cosec}{61}^{\circ }}+2\cot 8^{\circ }\cot {17}^{\circ }\cot {45}^{\circ }$ $\cot {73}^{\circ }\cot {82}^{\circ }-3(\sin {}^2{38}^{\circ }+\sin {}^2{52}^{\circ })$

Answer 1

$\frac{\sec {29}^0}{{cosec61}^0}+2{\cot 8}^0{\cot 17}^0\cot {45}^0\cot {73}^0\cot {82}^0-3({\sin }^2{38}^0+{\sin }^2{52}^0)$

$=\frac{cosec(90-61)}{cosec61}+2\tan (90-8)\tan (90-17)\cot {45}^0\cot {73}^0{\cot 82}^0-3({\sin }^2{38}^0+{\cos }^2(90-52))$

$=\frac{cosec61}{cosec61}+2{\tan 82}^0{\tan 73}^0\times 1\times {\cot 73}^0{\cot 82}^0-3({\sin }^2{38}^0+{\cos }^2{38}^0)$

$=1+2-3$

$=0$ (Answer)