-1sin x is real- ifA- x - -B- x -1-1-C- x-2 n-1 - - 2- n - ID- x - n - n - I

The correct option is C x=(2n+1)π/2, n∈Isec^ 1(sin x) is real, if sin x ≤ 1 or sin x ≥ 1 But 1 ≤ sin x ≤ 1 ∴ sec^ 1(sin x) is real only if sin x= 1 or 1 ⇒ x= ...

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Byju's Answer

Standard XII

Mathematics

Property 7

-1sin x is re...

Question

$s e c^{- 1}$ (sin x) is real, if

x∈(-∞, ∞)

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x∈[-1, 1]

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x=(2n+1)π/2, n∈I

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x=nπ, n∈I

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Solution

The correct option is C
x=(2n+1)π/2, n∈I

$s e c^{- 1} (s i n x)$ is real, if $s i n x \leq - 1$ or $s i n x \geq 1$
But $- 1 \leq s i n x \leq 1$
$∴ s e c^{- 1} (s i n x)$ is real only if
$s i n x = - 1 o r 1 \Rightarrow x = (2 n + 1) \frac{π}{2}, n ϵ I$

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Similar questions

L e t f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} (1 + | c o s x |)^{\frac{a b}{| c o s x |}}, & n π < x < (2 n + 1) \frac{π}{2} e^{a} . e^{b}, & x = (2 n + 1) \frac{π}{2} e^{\frac{c o t 2 x}{c o t 8 x}}, & (2 n + 1) \frac{π}{2} < x < (n + 1) π \end{matrix} I f f (x) i s c o n t i n u o u s i n ((n π), (n + 1) π, t h e n)

I f s i n^{10} x - c o s^{10} x = 1 t h e n x = (n ϵ Z)

Q. The vectors

\to b

and

\to c

are non-colinear, if

\to a \times (\to b \times \to c) + (\to a \cdot \to b) \to b = (4 - 2 x - sin y) \to b + (x^{2} - 1) \to c

and

(\to c \cdot \to c) \to a = \to c

then

Q. If

cos x = | sin x |

, then the general solution is

Q. Solve

cos 3 x + sin 2 x - sin 4 x = 0

, then

x = (2 n + 1) \frac{π}{m}, n \in I

n π + {(- 1)}^{n} \frac{π}{m}, n \in I

. Find the value of

m

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sec−1 (sin x) is real, if

The correct option is C x=(2n+1)π/2, n∈Isec−1(sin x) is real, if sin x≤−1 or sin x≥1 But −1≤sin x≤1 ∴sec−1(sin x) is real only if sin x=−1 or 1⇒x=(2n+1)π2,n ϵ I

$s e c^{- 1}$ (sin x) is real, if

The correct option is C
x=(2n+1)π/2, n∈I

$s e c^{- 1} (s i n x)$ is real, if $s i n x \leq - 1$ or $s i n x \geq 1$
But $- 1 \leq s i n x \leq 1$
$∴ s e c^{- 1} (s i n x)$ is real only if
$s i n x = - 1 o r 1 \Rightarrow x = (2 n + 1) \frac{π}{2}, n ϵ I$