Question 25 (Choice 1) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at April 16, 2024 by Teachoo

If sin(A+B) = 1 and cos (A - B)= √3/2, 0°< A+B ≤ 90° and A> B, then find the measures of angles A and B.

This question is Similar to Ex 8.2,3 - Chapter 8 Class 10

Transcript

Question 25 (Choice 1) If sin (A + B) = 1 and cos (A – B)= √("3" )/2, 0°< A + B ≤ 90° and A > B, then find the measures of angles A and B.Given that sin (A + B) = 1 But we know that sin 90° = 1 Thus, sin (A + B) = sin 90° ∴ A + B = 90° cos (A – B) = √𝟑/𝟐 But we know that cos 30° = √3/2 Thus cos (A – B) = cos 30° ∴ A – B = 30° Our equations are A + B = 90° …(1) A – B = 30° …(2) Adding (1) and (2) A + B + A – B = 90° + 30° 2A = 120° A = (120°)/2 A = 60° Putting A = 60° in (1) A + B = 90° 60° + B = 90° B = 90° − 60° B = 30° Hence A = 60° , B = 30°

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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