Question

Find the value of $\cos ({270}^o+\theta )\cos ({90}^o+\theta )-\cos ({270}^o+\theta )\cos \theta$.

Answer 1

We have,

$\Rightarrow \cos ({270}^{\circ }+\theta )\cos ({90}^{\circ }+\theta )-\cos ({270}^{\circ }+\theta )\cos \theta$

We know that

$\cos ({270}^{\circ }+\theta )=\sin \theta$

$\cos ({90}^{\circ }+\theta )=-\sin \theta$

Therefore,

$\Rightarrow \sin \theta (-\sin \theta )-\cos \theta \cos \theta$

$\Rightarrow -{\sin }^2\theta -{\cos }^2\theta$

$\Rightarrow -({\sin }^2\theta +{\cos }^2\theta )$

$\Rightarrow -1$

Hence, this is the answer.