Question

The given expression is $\sin \theta \cos ({90}^o-\theta )+\cos \theta \sin ({90}^o-\theta )+4$ equal to :

• A. $0$
• B. $5$
• C. $-5$
• D. $4$

Answer 1

The correct option is B $5$

Taking the given expression

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

We know that $\cos (90-\theta )=sin\theta ,sin(90-\theta )=cos\theta$

We get
$\sin \theta \sin \theta +\cos \theta \cos \theta +4$

${\sin }^2\theta +{\cos }^2\theta +4$ we know (${\sin }^2\theta +{\cos }^2\theta =1)$

$=1+4$

$=5$