Important Questions For Class 10 Maths Trigonometry | Q9

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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Video Explanation

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Explanatory Answer | Trigonometry Important Question 9

Given Data

sin (A + B) = 1
sin (A – B) =\\frac{1}{2})
0° < A + B ≤ 90°
∠A > ∠B

Compute A and B using sin (A + B) and sin (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)

Solve Equations (1) and (2) to Find A and B

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°