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If sin -1 x + sin -1 ⁡ y = 2π/3, then the value of cos -1 ⁡x + cos -1 ⁡y is

(a) 2π/3                 (b)  π/3              (c) π/2              (d) π

If sin^-1 x + sin^-1⁡ y = 2pi/3, then value of cos-1 ⁡x + cos-1 ⁡y is

Question 6 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Question 6 If sin^(−1)⁡𝑥+sin^(−1)⁡𝑦=2𝜋/3, then the value of cos^(−1)⁡𝑥+cos^(−1)⁡𝑦 is (a) 2𝜋/3 (b) 𝜋/3 (c) 𝜋/2 (d) 𝜋 We know that cos^(−1)⁡𝑥+sin^(−1)⁡𝑥=𝜋/2 And similarly cos^(−1)⁡𝑦+sin^(−1)⁡𝑦=𝜋/2 Adding both equations cos^(−1)⁡𝑥+sin^(−1)⁡𝑥+cos^(−1)⁡𝑦+sin^(−1)⁡𝑦=𝜋/2+𝜋/2 cos^(−1)⁡𝑥+cos^(−1)⁡𝑦+〖𝒔𝒊𝒏〗^(−𝟏)⁡𝒙+〖𝒔𝒊𝒏〗^(−𝟏)⁡𝒚=𝜋 Putting value of 〖𝑠𝑖𝑛〗^(−1)⁡𝑥+〖𝑠𝑖𝑛〗^(−1)⁡𝑦=2𝜋/3 〖𝑐𝑜𝑠〗^(−1)⁡𝑥+〖𝑐𝑜𝑠〗^(−1)⁡𝑦+2𝜋/3=𝜋 〖𝑐𝑜𝑠〗^(−1)⁡𝑥+〖𝑐𝑜𝑠〗^(−1)⁡𝑦=𝜋−2𝜋/3 〖𝑐𝑜𝑠〗^(−1)⁡𝑥+〖𝑐𝑜𝑠〗^(−1)⁡𝑦=𝜋/3 So, the correct answer is (b) - 𝝅/𝟑 1 mark

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.