Question

Solve the equation:-
$\frac{\cos {35}^{\circ }}{\sin {55}^{\circ }}+\frac{\sin {11}^{\circ }}{\cos {79}^{\circ }}\cos {28}^{\circ }\text{cosec}{62}^{\circ }$

Answer 1

$\frac{\cos {35}^o}{\sin {55}^o}+\frac{\sin {11}^o}{\cos {69}^o}\cos {28}^{o}cosec{62}^o$

By using concept of complementary angles,

$\frac{\cos {35}^o}{\sin {55}^o}+\frac{\sin {11}^o}{\cos {69}^o}\cos {28}^{o}cosec{62}^o$

$\frac{\cos {35}^o}{\cos {35}^o}+\frac{\sin {11}^o}{\sin {11}^o}\cos {28}^o\sec {28}^o$

(Because, we know that)

$\sin (90-\theta )=\cos \theta$

$\cos (90-\theta )=\sin \theta$

$cosec(90-\theta )=\sec \theta$

$1+1\cos {28}^o\sec {28}^o$

Now, we know that

$\sec \theta =\frac{1}{\cos \theta }$

$1+1\cos {28}^o\frac{1}{\cos {28}^o}=1+1.1=1+1=2$