Q) If sin(A + B) = 1 and cos (A − B) = √3/ 2 ,0° < A, B < 90°, find the measure of angles A and B.

[Q 22 – Sample Question Paper – CBSE Board 2026]

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

sin (A + B) = 1

Since we know that sin 90⁰ = 1

∴ sin (A + B) = sin 90⁰

∴ A + B = 90⁰ ……………….. (i)

Next, we have: cos (A – B) =

Since, cos 30⁰ =

∴ cos (A – B) = cos 30⁰

∴ A – B = 30⁰ …………(ii)

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

(A + B) + ( A – B) = 90⁰ + 30⁰

∴ 2 A = 120⁰

∴ A = 60⁰

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

A + B = 90⁰

∴ 60⁰ + B = 90⁰

∴ B = 90⁰ – 60⁰

∴ B = 30⁰

Since above values of angles A and B are < 0⁰ and > 90⁰, hence, our values are correct.

Therefore the values of A and B are 60⁰ and 30⁰ respectively.

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