Question

Sin-1x+tan-1x=pi/2 solve

Answer 1

this is your answer I hope you will be satisfied and mark as a brainlist

Answer 2

x  =  √ ((√5 - 1 )/2)

Step-by-step explanation:

Sin⁻¹x  + Tan⁻¹x  = π/2

=>  Tan⁻¹x = π/2 - Sin⁻¹x

Taking Cos Both sides

=> Cos(Tan⁻¹x)  = Cos(π/2 - Sin⁻¹x)

=>  Cos(Tan⁻¹x)  = Sin(Sin⁻¹x)

Sin(Sin⁻¹x) = x

Sec²α = Tan²α + 1   => Cos²α = 1/(1 + Tan²α)  

Cos(Tan⁻¹x)  = √1/(1 + x²)

=> √1/(1 + x²)  = x

Squaring both sides

=> 1/(1 + x²) = x²

=> x²(1 + x²) = 1

=> (x²)²  + x²  - 1 = 0

=> x²  =  (-1  ± √(1 + 4) )/2

=> x² = (√5- 1 )/2  as x² can not be -ve

x  =  √ ((√5 - 1 )/2)

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