Given 0 - x -1-2 then the value of tan - sin-1x-2-1-x2-2-sin-1x - is

X=sin θ⇒ tan [sin^ 1(sin (θ +π/4 ) ) θ ]=1 ...

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Composition of Trigonometric Functions and Inverse Trigonometric Functions

Given 0 ≤ x ≤...

Question

Given $0 \leq x \leq \frac{1}{2}$ then the value of $t a n [s i n^{- 1} {\frac{x}{\sqrt{2}} + \frac{\sqrt{1 - x^{2}}}{\sqrt{2}}} - s i n^{- 1} x]$ is

-1

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\frac{1}{\sqrt{3}}

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\sqrt{3}

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Similar questions

{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

0 \leq x \leq \frac{1}{2}

t a n [{s i n}^{- 1} {\frac{x}{\sqrt{2}} + \frac{\sqrt{1 - x^{2}}}{\sqrt{2}}} - {s i n}^{- 1} x]

α = {s i n}^{- 1} \frac{4}{5} + {s i n}^{- 1} \frac{1}{3}

β = {c o s}^{- 1} \frac{4}{5} + {c o s}^{- 1} \frac{1}{3}

x \geq 1 t h e n 2 t a n^{- 1} x + s i n^{- 1} (\frac{2 x}{1 + x^{2}})

{cot}^{- 1} (\frac{1}{x}) + {cos}^{- 1} (- x) + {tan}^{- 1} x = π

{sin}^{- 1} x < 0,

\frac{(1 - x^{2})^{3 / 2}}{x^{2}}

s i n^{- 1} \sqrt{x^{2} + 2 x + 1} + s e c^{- 1} \sqrt{x^{2} + 2 x + 1} = \frac{π}{2}, x \neq 0

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{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}^{- 1} x + {c o s}^{- 1} [\frac{x}{2} + \frac{\sqrt{(3 - 3 x^{2})}}{2}]

(\frac{1}{2} \leq x \leq 1)

c o s (2 {c o s}^{- 1} x + {s i n}^{- 1} x)

x = 1 / 5

0 \leq {c o s}^{- 1} x \leq π

- π / 2 \leq {s i n}^{- 1} x \leq π / 2

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