Question

If $tanA=1andtanB=\sqrt{3}$, evaluate $cosAcosB-sinAsinB$.

• A. $\frac{1-\sqrt{3}}{2\sqrt{2}}$
• B. $1$
• C. $0$
• D. $1-\sqrt{3}$

Answer 1

Answer: (A)

$\frac{1-\sqrt{3}}{2\sqrt{2}}$

Given,

$\tan A=1$

$\Rightarrow A={45}^{\circ }$

$\tan B=\sqrt{3}$

$\Rightarrow B={60}^{\circ }$

$\cos A\cos B-\sin A\sin B$

$=\cos 45\cos 60-\sin 45\sin 60$

$=\frac{1}{\sqrt{2}}\frac{1}{2}-\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}$

$=\frac{1-\sqrt{3}}{2\sqrt{2}}$