Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

If $\cos A\cos B+\sin A\sin B\sin C=1$, then?

• A. $a=b$
• B. $c=\sqrt{2}b$
• C. $c=\sqrt{2}a$
• D. $a=c$

Answer 1

Answer: (A), (B), (C)

$a=b$
$c=\sqrt{2}b$
$c=\sqrt{2}a$

for $\angle A=45°,\angle B=45°and\angle C=90°\cos A\cos B+\sin A\sin B\sin C=1$

$\therefore \frac{\sin 45°}{a}=\frac{\sin 45°}{b}=\frac{\sin 90°}{c}$

$a=b$, clearly

Hence, a=b is correct

$\frac{\frac{1}{\sqrt{2}}}{b}=\frac{1}{2}c=\sqrt{2}b$

Hence , $c=\sqrt{2}b$ is correct.

$\frac{\frac{1}{\sqrt{2}}}{a}=\frac{1}{c}c=\sqrt{2}a$

Hence, $c=\sqrt{2}a$ is correct.