Q) If 2 sin (A + B) = √3 and cos (A – B) = 1 , then find the measures of angles A and B. 0 <= A B, (A + B) <= 90 deg

Ans: Let’s take each of the given values one by one:

2 sin(A + B) = √3

∴ sin (A + B) =

Since we know that sin 60⁰ =

∴ sin (A + B) = sin 60⁰

∴ A + B = 60⁰ ……………….. (i)

This also satisfies our given condition that A + B <= 90

Next, we have:

cos(A – B) = 1

Since, cos 0 = 1

∴ cos (A – B) = cos 0

∴ A – B = 0 …………(ii)

By adding equations (i) and (ii), we get:

(A + B) + ( A – B) = 60⁰ + 0

∴ 2 A = 60⁰

∴ A = 30⁰

By substituting the value of A in equation (i) , we get:

A + B = 60⁰

∴ 30 + B = 60⁰

∴ B = 30⁰

Therefore the values of A and B are 30⁰ each.

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