Without using tables or calculator, evaluate

Question 1

Question 2

Question:- Find the value

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

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

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

So putting down the value

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

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

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

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