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

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.