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

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.