Question

The value of $\sin ({90}^o-\theta )\cos \theta +\cos ({90}^o-\theta )\sin \theta$ is

• A. $1$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is A $1$

The value of $\sin ({90}^o-\theta )\cos \theta +\cos ({90}^o-\theta )\sin \theta$

$=\cos \theta .\cos \theta +\sin \theta .\sin \theta$ .... $[$ Since $\sin (90-a)=\cos a$and $\cos (90-a)=\sin a]$

$={\cos }^2\theta +{\sin }^2\theta$

$=1$ .... $[$ Since ${\sin }^{2}a+{\cos }^{2}a=1]$