Question

sin inverse X + Sin inverse 1 - X equal to Cos inverse X find the value of x​

Answer 1

I hope this would help you.....

Answer 2

it is given that, sin-¹x + sin-¹(1 - x) = cos-¹x

we have to find the value of x.

sin-¹x + sin-¹(1 - x) = cos-¹x = sin-¹√(1 - x²)

⇒sin-¹(x √{1 - (1 - x)²} + (1 - x)√(1 - x²) = sin-¹√(1 - x²)

⇒x√{1 - 1 - x² + 2x} + (1 - x)√(1 - x²) = √(1 - x²)

⇒x√(2x - x²) = (- x)√(1 - x²)

squaring both sides we get,

⇒x²(2x - x²) = (- x)²(1 - x²)

⇒2x³ - x⁴ = x² - x⁴

⇒2x³ = x²

⇒x = 0, 1/2

hence value of x = 0, 1/2

also read similar questions : 1+cos x+sin x/1+cos x-sin x = 1+sin x/cos x.

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