Question

If A and B are positive acute angles satisfying the equalities 3cos? A + 2cos?B=4 and 3 sin A
2 cos B
thenA+2B is equal
to
sin B
COS A 2
​

Answer 1

Given: A and B are positive acute angles satisfying the equalities

3 cos^2 A+ 2cos^2 B = 4  and 3sinA / sinB = 2cosB / cosA

To find: The value of A + 2B?

Solution:

• Now we have given the following equalities as:

                  3 cos^2 A + 2cos^2 B = 4

                  2cos^2 B - 1 = 4 - 3 cos^2 A - 1

                  cos 2B = 3  - 3 cos^2 A

                  cos 2B = 3 ( 1 - cos^2 A)

                  cos 2B = 3 sin^2 A     .......................(i)

• Now we have another inequality as:

                  3sinA / sinB = 2cosB / cosA

                  sin 2B = 3 sin A cos A  ......................(ii)

• Now we know that

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

• Now putting (i) and (ii) in above equation, we get:

                  cos (A + 2B) = cos A(3 sin^2 A) - sin A( 3 sin A cos A)

                  cos (A + 2B) = 0

                  A + 2B = π/2

Answer:

             So the value of A + 2B is π/2.