Question

The value of $\cos \left(270°+\theta \right)\cos \left(90°-\theta \right)-\sin \left(270°-\theta \right)\cos \left(\theta \right)$ is

• A. $0$
• B. $-1$
• C. $\frac{1}{2}$
• D. $1$

Answer 1

The correct option is D

$1$

Explanation for correct option

The value of $\cos \left(270°+\theta \right)\cos \left(90°-\theta \right)-\sin \left(270°-\theta \right)\cos \left(\theta \right)$

$=$$\sin \left(\theta \right)\sin \left(\theta \right)-\left(-\cos \left(\theta \right)\right)\cos \left(\theta \right)$

$$\begin{gathered} ={\sin }^2\left(\theta \right)+{\cos }^2\left(\theta \right) \\ =1 \end{gathered}$$

Hence, the correct option is $\mathrm{Option}\left(\mathrm{D}\right)$