The equation x + x = 2has - Vidyadip

MCQ

The equation $\sin x + \cos x = 2$has

A
One solution
B
Two solutions
C
Infinite number of solutions
✓
No solutions

✓

Answer

Correct option: D.

No solutions

d
(d) No solution as $|\sin x| \le 1,\,|\cos x| \le 1$ and both of them do not attain their maximum value for the same angle.

Aliter : Since the maximum value of $(\sin x + \cos x) = \sqrt {{1^2} + {1^2}} = \sqrt 2 $.

Hence there is no satisfying $\sin x + \cos x = 2$.

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 "MCQ" from Trigonometrical equations→Trigonometrical equations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\tan\alpha=\frac{\text{x}}{\text{x}+1}\text{ and }\tan\beta=\frac{1}{2\text{x}+1},$ than $\alpha+\beta$ is equal to

The number of integral values of $k$, for which the equation $7\cos x + 5\sin x = 2k + 1$ has a solution, is

The greatest coefficient in the expansion of ${(1 + x)^{2n + 1}}$ is

The average age of 6 students is 11 years. If two more students of age 14 and 16 years join, their average will become

Let $\Delta = \left| {\,\begin{array}{*{20}{c}}1&\omega &{2{\omega ^2}}\\2&{2{\omega ^2}}&{4{\omega ^3}}\\3&{3{\omega ^3}}&{6{\omega ^4}}\end{array}\,} \right|$ where $\omega $ is the cube root of unity, then

If the coordinates of a point be given by the equations $x = b\sec \phi ,\;\;y = a\tan \phi $, then its locus is

A point $P$ is taken outside $\Delta ABC$ where $(B(1, \sqrt 3 ), A(0, 0)$ and $C(2, 0))$ , but inside the acute angle $BAC$ , such that $\angle APC = \frac{\pi }{6}$ and $\angle BPA = \frac{\pi }{{12}}$ . Slope of the line $BP$ is

${(1 + i)^{10}}$, where ${i^2} = - 1,$ is equal to

An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is

If $\tan \theta = - \frac{1}{{\sqrt {10} }}$ and $\theta $ lies in the fourth quadrant, then $\cos \theta = $