Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation cos^-1(x)-2sin^-l(x) = cos^-1(2x) is equal to :

Question

Accepted Answer

Correct answer: A. (a) Let, sin^-1x=0 Then, cos^-1x= 2- Given : cos^-1x-2 sin^-1x= cos^-1 (2x ) So, 2-3 = cos^-1 (2x ) Taking cosine: 2x= cos( 2-3 )= sin3 Since x= sinθ, 2 sinθ= sin3 2 sinθ=3 sinθ-4 sin^3 sinθ(1-4 sin^2 )=0 Thus, x=0 ,x= 12 ,x=- 12 All satisfy the original equation. Therefore, sum of all solutions: 0+ 12- 12=0

$Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation co s^{- 1} (x)- 2 s i n^{- l} (x) = co s^{- 1} (2x) is equal to :$

Solution

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