If tan A = 1 and tan B = 3 Find: 1) cos A cos B - sin A - Maths - Trigonometry

Question

If tan A = 1 and tan B = ?3
Find:
1) cos A cos B - sin A sin B
2) sin A cos B + cos A sin B

Pranay Loya · Accepted Answer

Dear Student!

Here is the answer to your query.

Given : tan A = 1 and tan B = $\sqrt{3}$

∴ A = 45° and B = 60° ( tan 45° = 1 and tan 60° = $\sqrt{3}$ )

(1) cos A cos B – sin A sin B

= cos 45° cos 60° – sin 45° sin 60°

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

(2) sin A cos B + cos A sin B

= sin 45° cos 60°+ cos 45° sin 60°

$= \frac{1}{\sqrt{2}} \times \frac{1}{2} + \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} = \frac{1 + \sqrt{3}}{2 \sqrt{2}}$

Cheers!

If tan A = 1 and tan B = ?3 Find: 1) cos A cos B - sin A sin B 2) sin A cos B + cos A sin B