Question

Without using tables or calculator, evaluate​

Answer 1

Question:- Find the value

`( \sin(20 \degree) )/( \cos(70\degree) ) + ( \cos(35\degree) )/( \sin( 65\degree))`

Answer->

`( \sin(20 \degree) )/( \cos(70\degree) ) + ( \cos(35\degree) )/( \sin( 65\degree))`

we know:-

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

So putting down the value

`( \cos(90 - 20 \degree) )/( \cos(70\degree) ) + ( \sin(90 - 35\degree) )/( \sin( 65\degree))`

`( \cos(70\degree) )/( \cos(70\degree) ) + ( \sin(65\degree) )/( \sin( 65\degree))`

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

`(1)/(1) + (1)/(1) \\ 1 + 1 = 2 \: \: ans`