Question

Without using tables or calculator, evaluate​

Answer 1

Question:- Find the value

$\frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)}$

Answer->

$\frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)}$

we know:-

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

So putting down the value

$\frac{ \cos(90 - 20 \degree) }{ \cos(70\degree) } + \frac{ \sin(90 - 35\degree) }{ \sin( 65\degree)}$

$\frac{ \cos(70\degree) }{ \cos(70\degree) } + \frac{ \sin(65\degree) }{ \sin( 65\degree)}$

$\frac{\cancel{\cos(70\degree)}}{ \cancel{\cos(70\degree)}} + \frac{\cancel{\sin(65\degree)}}{\cancel{\sin( 65\degree)}}$

$\frac{1}{1} + \frac{1}{1} \\ 1 + 1 = 2 \: \: ans$