Question

STATEMENT - 1 : $cos{15}^{\circ }=\frac{\sqrt{3}+1}{2\sqrt{2}}$
STATEMENT - 2 : $cos(A-B)=cosAcosB+sinAsinB$

• A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
• B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
• C. Statement - 1 is True, Statement - 2 is False
• D. Statement - 1 is False, Statement - 2 is True

Answer 1

The correct option is A Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

Putting $A={45}^{\circ }$ and $B={30}^{\circ }$
We get $cos({45}^{\circ }-{30}^{\circ })=cos{45}^{\circ }cos{30}^{\circ }+sin{45}^{\circ }sin{30}^{\circ }$
$=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}=\frac{\sqrt{3}+1}{2\sqrt{2}}$