Question

Prove that ,

cos-^1(x) + cos^-1y = cos^-1 |xy -√(1-x²)(1-y²) |

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Answer 1

Hii

Step-by-step explanation:

#Answerwithquality#BAL

Solution is in this given attachment !

Hope it's helpful

Answer 2

Answer:

Let x = cosa and y = cos b

(1- x^2) = 1 - cos^2 a = sin^2 a

(1-y^2) = 1 - cos^2 b = sin^2 b

Now,

cos^-1 ( xy - √(1-x^2)(1-y^2))

= cos^-1 ( cosa cos b - √(sin^2a)(sin^2b)

= cos^-1 ( cos acosb - sina sin b)

= cos^-1 ( cos ( a+ b)

= a+ b

As x= cos a and y= cosb

So, a = cos ^-1 x b = cos^ -1 y

= cos^-1 x + cos^-1 y

hence proved