Question

Show that: $\sin \left(\frac{\pi }{2}-\theta \right)=\cos \theta$

Answer 1

$\sin (\frac{\pi }{2}-\theta )=\sin \frac{\pi }{2}\cos \theta -\cos \frac{\pi }{2}\sin \theta$

[By $\sin (a-b)=\sin a\cos b-\cos a\sin b$]

$\therefore \sin (\frac{\pi }{2}-\theta )=\cos \theta -0$

$=\cos \theta$ Hence proved