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
CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
Last updated at April 16, 2024 by Teachoo
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