Question

$\ln \Delta ABC$, if $\cos A\cos B+\sin A\sin B\sin C=1$, then $a:b:c$ is equal to

• A. $1:1:2$
• B. $1:1:\sqrt{2}$
• C. $1:\sqrt{2}:1$
• D. $\sqrt{2}:1:2$

Answer 1

The correct option is B $1:1:\sqrt{2}$

$\sin C=\frac{1-\cos A\cos B}{\sin A\sin B}$

$\frac{a}{\sin A}$ = $\frac{b}{\sin B}$ = $\frac{c}{\sin C}$ = $q$ (constant)

$a:b:c=\sin A:\sin B:\sin C$

By replacing A and B the equation does't change hence ratio of A and B are same

and therefore,

$a:b:c=1:1:\sqrt{2}$