Question

If ${\sin }^2\theta +{\sin }^2\varphi =1/2,{\cos }^2+{\cos }^2\varphi =3/2$, then ${\cos }^2(\theta -\varphi )$ is equal to

• A. 3/8
• B. 5/8
• C. 3/4
• D. 5/4

Answer 1

Answer: (B)

Using cosine formula
$2\sin (\theta +\varphi )\cos (\theta -\varphi )=1/2$ ......(i)
$2\cos (\theta +\varphi )\cos (\theta -\varphi )=3/2$ .....(ii)
Squaring (1) and (2) and then adding
$4{\cos }^2\left(\theta -\varphi \right)=\frac{1}{4}+\frac{9}{4}=\frac{5}{2}$
$\Rightarrow {\cos }^2\left(\theta -\varphi \right)=\frac{5}{8}$