This class 10 Maths extra question is from the chapter 8, Introduction to Trigonometry. Concept Tested: Calculation of angles using information about trigonometric values of sum and difference of two angles and solving a pair of linear equations in two variables. An important question in trigonometry.

Question 9: sin (A + B) = 1 and sin (A – B) =\\frac{1}{2}); (0° < (A + B) ≤ 90°); (∠A > ∠B). Find ∠A and ∠B.

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sin (A + B) = 1

sin (A – B) =\\frac{1}{2})

0° < A + B ≤ 90°

∠A > ∠B

sin (A + B) = 1

We know sin 90° = 1

∴ sin (A + B) = sin 90°

**A + B = 90°** ......(1)

sin (A – B) = \\frac{1}{2})

We know sin 30° =\\frac{1}{2})

∴ sin (A – B) = sin 30°

**A – B = 30°** ...... (2)

**Add equations (1) and (2)**: (A + B) + (A – B) = 90° + 30°

2A = 120° or A = 60°

Substitute A = 60° in **equation 1**

60° + B = 90°

Or B = 90° – 60° ⇒ B = 30°

So, **∠A = 60° and ∠B = 30°**

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CBSE Class 10 Maths - 2021

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