If ( )= ( ), then 2x= - Vidyadip

MCQ

If $\sin(\pi\cos\text{x})=\cos(\pi\sin\text{x}),$ then $\sin2\text{x}=$

A
$\pm\frac34$
B
$\pm\frac43$
✓
$\pm\frac13$
D
None of these

✓

Answer

Correct option: C.

$\pm\frac13$

$\sin(\pi\cos\text{x})=\cos(\pi\sin\text{x})$
As we know that $\sin\text{x}=-\cos\Big(\frac\pi2+\text{x}\Big)$
$\Rightarrow-\cos\Big(\frac\pi2+\pi\cos\text{x}\Big)=\cos(\pi\sin\text{x})$
$\Rightarrow\frac{-\pi}{2}-\pi\cos\text{x}=\pi\sin\text{x}$
$\Rightarrow\pi\sin\text{x}-\pi\cos\text{x}=\frac12$
$\Rightarrow\sin\text{x}-\cos\text{x}=\frac12$
Squaring both sides we get,
$\Rightarrow\sin^2\text{x}+\cos^2\text{x}+2\sin\text{x}\cos\text{x}=\frac14$
$\Rightarrow1+\sin2\text{x}=\frac{1}{4}$
$\Rightarrow\sin2\text{x}=\frac13$
$\therefore\sin2\text{x}=\pm\frac13$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If $-2<2\text{x}-1<2$ then the value of $x$ lies in the interval:

Team $'A'$ consists of $7$ boys and $n$ girls and Team $'B'$ has $4$ boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to

Equation of the line passing through $(1, 2)$ and parallel to the line $y = 3x - 1$ is:

The probability of solving a question by three students are $\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}$ respectively. Probability of question is being solved will be

Let $S(K) = 1+ 3 + 5…+ (2K-1) = 3+ K^2$. Then which of the following is true:

Let $E$ = $x^{2017} + y^{2017} + z^{2017} -2017xyz$ (where $x, y, z \geq 0$ ), then the least value of $E$ is

If the arithmetic mean of $7, 8, x, 11, 14$ is $x,$ then $x:$

If the sum of series $\frac{1}{1 \cdot(1+d)}+\frac{1}{(1+d)(1+2 d)}+\ldots \ldots+\frac{1}{(1+9 d)(1+10 d)}$ is equal to $5$ , then $50 \mathrm{~d}$ is equal to :

The normal meet the parabola ${y^2} = 4ax$ at that point where the abissiae of the point is equal to the ordinate of the point is

If $x + iy =\sqrt {\phi + i\psi } \,$ where $ i = \sqrt { - 1} \,$ and $\phi$ and $\psi$ are non zero real parameters then $ \phi =$ constant and $ \psi = $ constant, represents two systems of rectangular hyperbola which intersect at an angle of