Q) If sin (A – B) = , cos (A + B) = ; 0 < A + B <= 90°, A > B; find ∠ A and ∠ B.

Ans: Let’s take the components one by one:

Step 1: sin (A – B) =

Since we know that sin 30⁰ =

∴ sin (A – B) = sin 30⁰

∴ A – B = 30⁰  …… (i)

Step 2: cos (A + B) = ;

Since we know that cos 60⁰ =

∴ cos (A + B) = cos 60⁰

∴ A + B = 60⁰   …… (ii)

Step 3: By adding equation (i) and (ii), we get:

∴ (A – B) + (A + B) = 30⁰ + 60⁰

∴ 2 A = 90⁰

∴ A = = 45⁰

By putting the value of A into equation (i), we get:

A – B = 30⁰ 

∴ 45⁰ – B = 30⁰

∴ B = 45⁰ – 30⁰

∴ B = 15⁰

Therefore the values of A is 45⁰ and value of B is 15⁰ .

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