We need to find out the reason for cos (90-x)= sin x and (sin (90-x)=cos x
Solution
We can get these by the cartesian quadrant graph or by trigonometric identity
We know the trigonometric identity that
\(\cos (\alpha -\beta )=\cos \alpha \cos \beta +\sin \alpha \sin \beta\)——————(i) \(\\sin (\alpha -\beta )=\sin \alpha \cos \beta -\cos \alpha \sin \beta\)—————–(ii)Using equation (i)
\(\cos (90-x )=\cos 90\cos x+\sin 90 \sin x\)On substituting cos 90 value as 0 and sin 90 as 1 we get,
\(\cos (90-x )=0\cos x+1 \sin x\) \(\cos (90-x )=\sin x\)Similarly, on solving (ii) we get
\(\sin (90-x )=\cos x\)Hence proved
