Question

How do you verify `sinx=cos(pi/2 - x)`?

Answer 1

see below

Explanation:

In the above figure `Delta`ABC is a rt angled triangle where `/_ABC=pi/2`,`/_BAC=x`and `/_ACB=pi/2-x`

Now `cos/_ACB=(BC)/(AC)` ( side opposite to the angle considered for trigonometric ratio is taken as perpendicular and the side lying vertical to it is taken as base)
`=>cos(pi/2-x)=(BC)/(AC)`

Again `sin/_CAB=(BC)/(AC)`
`=>sinx=(BC)/(AC)`
Comparing these two relation we can say
`sinx=cos(pi/2-x)`