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Solution - Prove that tan^(-1) [(√(1+x)-√(1-x))/(√(1+x)+√(1-x))]=pi/4-1/2 cos^(-1)x,-1/√2<=x<=1 - Inverse Trigonometric Functions (Simplification and Examples)

ConceptInverse Trigonometric Functions (Simplification and Examples)

Question

Prove that

`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`

Solution

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Reference Material

Solution for question: Prove that tan^(-1) [(√(1+x)-√(1-x))/(√(1+x)+√(1-x))]=pi/4-1/2 cos^(-1)x,-1/√2<=x<=1 concept: Inverse Trigonometric Functions (Simplification and Examples). For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)
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