Write the expression sin(sin^-1 (√(3) / 2) - tan^-1 (x) as an algebraic expression involving no trigonometric functions. You don’t need to rationalize the denominator.

Question

Write the expression
`sin(sin^-1 (√(3) / 2) - tan^-1 (x)` as an algebraic expression involving no trigonometric functions. You don’t need to rationalize the denominator.

Answer 1

Explanation:

`let~sin ^(-1)(√(3) /2)=y\\sin y=√(3) /2=sin ~(\pi /3),sin (\pi -\pi /3)\\y=\pi /3,2 \pi /3`

`sin ^(-1)(√(3) /2)=\pi /3,2\pi /3`

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