Question

If π/2 < sin-1 < π/2 , then tan (sin-1x) is equal to

Answer 1

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Hypothesis : -π/2 < X < π/2

By applying Sin-1 in all sides of this inequality we derive,

sin-1 -π/2 < sin-1x < sin-1 π/2

This implies,

-1<sin-1x<1

By applying tan ratio on all sides we get,

tan(-1)< tan(sin-1x) < tan(1)

This implies,

-1 < tan(sin-1x) <1

Thus hereby we conclude that value of tan(sin-1x) lies between the interval (-1,1)

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