Number of solutions to the equation cos - 1x - sin - 1 x2 - -6 is-are

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Basic Inverse Trigonometric Functions

Number of sol...

Question

Number of solution(s) to the equation ${cos}^{- 1} x + {sin}^{- 1} (\frac{x}{2}) = \frac{π}{6}$ is/are

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c o s^{- 1} (\frac{1 + x^{2}}{2 x}) - c o s^{- 1} x = \frac{π}{2} + s i n^{- 1} x

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

x \in [- π, 3 π]

cos \frac{(\sqrt{2} + 1) x}{2} cos \frac{(\sqrt{2} - 1) x}{2} = 1

{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

(s i n^{- 1} x)^{3} + (c o s^{- 1} x)^{3} - a π^{3} = 0

a ⩾ \frac{1}{32} .

x ϵ R, s i n^{- 1} x + c o s^{- 1} x = \frac{π}{2}

0 \leq (s i n^{- 1} x - \frac{π}{4})^{2} \leq \frac{9 π^{2}}{16}

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