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Derivative of One Function w.r.t Another

15. If 1/2 si...

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15. If 1/2 sin inverse [3sin2theta/5+4cos2theta]=tan inverse x then x=?

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Q. Inverse circular functions,Principal values of

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

.

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

c o s (2 {s i n}^{- 1} x) = 1 / 9

{c o s}^{- 1} (3 / 5) - {s i n}^{- 1} (4 / 5) = {c o s}^{- 1} x

s i n ({s i n}^{- 1} \frac{1}{5} + {c o s}^{- 1} x) = 1

, then prove that x is equal to

1 / 5

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Derivative of One Function w.r.t Another

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