if cos(A - B) = (√(3))/2 and cot (A + B) = 1/(√(3)) , where A - B and A + B are acute angles, then (2A -3B) is equal to:

if cos(A - B) = (√(3))/2 and cot (A + B) = 1/(√(3))…

if cos(A - B) = $\frac{\sqrt{3}}{2}$ and cot (A + B) = $\frac{1}{\sqrt{3}}$ , where A - B and A + B are acute angles, then (2A -3B) is equal to:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e 45°.

Here it is given that,

cos (A - B) = $\frac{\sqrt{3}}{2}$ $\Rightarrow cos \ (A - B) = cos \ 30°$

So (A - B) = 30°........(1)

cot (A + B) = $\frac{1}{\sqrt{3}}$ $\Rightarrow cot(A + B) = cot \ 60°$

So (A + B) = 60°.......(2)

On solving equation (1) and (2) one get

A = 45° and B = 15°

Now the required value of (2A - 3B) = (90 - 45) = 45°