The equation sin -1 x-cos -1 x-cos -1-3-2 has

The correct option is C Unique solutionWe hav sin^ 1 x cos^ 1 x = cos^ 1√(3)/2 = π/6 But sin^ 1 x + cos^ 1 x = π/2 ∴ sin^ 1 x = π/3 and cos^ 1 x = π/6 ⇒ x = ...

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Standard XII

Mathematics

One - One function

The equation ...

Question

The equation $s i n^{- 1} x - c o s^{- 1} x = c o s^{- 1} (\frac{\sqrt{3}}{2})$ has

No solution

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Unique solution

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Infinite number of solutions

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None of these

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Solution

The correct option is B
Unique solution

We hav $s i n^{- 1} x - c o s^{- 1} x = c o s^{- 1} \frac{\sqrt{3}}{2} = \frac{π}{6} B u t s i n^{- 1} x + c o s^{- 1} x = \frac{π}{2} ∴ s i n^{- 1} x = \frac{π}{3} a n d c o s^{- 1} x = \frac{π}{6} \Rightarrow x = \frac{\sqrt{3}}{2}$ is the unique solution.

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Similar questions

Q. The equation 2

{cos}^{- 1} x + {sin}^{- 1} x = \frac{11 π}{6}

has

Q. Let

α, β (α > β)

be the roots of the equation

{sin}^{- 1} x - \frac{1}{{sin}^{- 1} x} = {cos}^{- 1} x - \frac{1}{{cos}^{- 1} x} .

Then

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

.
(a) Solve the equation :

{c o s}^{- 1} (\sqrt{6} x) + {c o s}^{- 1} (3 \sqrt{3} x^{2}) = \frac{π}{2}

(b) If

{s i n}^{1} 6 x + {s i n}^{- 1} 6 \sqrt{3} x = - π / 2

, then

x = . . . . . . .

(c)

{s i n}^{- 1} x + {s i n}^{- 1} 2 x = π / 3

Q. Statement I : The equation

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

has a solution for all

a ⩾ \frac{1}{32} .

Statement II : For any

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

and

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

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

Evaluate

(a)

{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)

(b)

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

x = 1 / 5

where

0 \leq {c o s}^{- 1} x \leq π

and

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

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The equation sin−1x−cos−1x=cos−1(√32) has

The correct option is B Unique solutionWe hav sin−1x−cos−1x=cos−1√32=π6Butsin−1x+cos−1x=π2∴sin−1x=π3 and cos−1x=π6⇒x=√32 is the unique solution.

The equation $s i n^{- 1} x - c o s^{- 1} x = c o s^{- 1} (\frac{\sqrt{3}}{2})$ has