The equation 2 ^ - 1 x + ^ - 1 x = 11 6 has - Vidyadip

MCQ

The equation $2{\cos ^{ - 1}}x + {\sin ^{ - 1}}x = \frac{{11\pi }}{6}$ has

✓
No solution
B
Only one solution
C
Two solutions
D
Three solutions

✓

Answer

Correct option: A.

No solution

a
(a) Given equation is $2{\cos ^{ - 1}}x + {\sin ^{ - 1}}x = \frac{{11\pi }}{6}$

==> ${\cos ^{ - 1}}x + ({\cos ^{ - 1}}x + {\sin ^{ - 1}}x) = \frac{{11\pi }}{6}$

==> ${\cos ^{ - 1}}x + \frac{\pi }{2} = \frac{{11\pi }}{6}$

$ \Rightarrow {\cos ^{ - 1}}x = 4\pi /3$

which is not possible as ${\cos ^{ - 1}}x \in [0,\,\pi ]$.

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