Equation sin x + cos x = 2 has

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Trigonometrical Equations

easy

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

A

One solution

B

Two solutions

C

Infinite number of solutions

D

No solutions

Solution

(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 $\sin x + \cos x = 2$.

Standard 11

Mathematics

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