Trigonometric Equations Question 27
Question: The equation $ \sin x+\cos x=2 $ has
[EAMCET 1986; MP PET 1998; Pb. CET 1993]
Options:
A) One solution
B) Two solutions
C) Infinite number of solutions
D) No solutions
Show Answer
Answer:
Correct Answer: D
Solution:
- 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 $ x $ satisfying $ \sin x+\cos x=2 $ .
BETA
