COMEDK · Maths · 9. Trigonometric Equations
The number of solution of \(\cos ^2 x=3-3 \sin x\) \(\forall x \in[0,2 \pi]\) is
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \(\cos ^2 x=3-3 \sin x\) \(\begin{aligned} & 1-\sin ^2 x=3-3 \sin x \\ & \sin ^2 x-3 \sin x+2=0 \\ & (\sin x-1)(\sin x-2)=0 \\ & \therefore \quad \sin x-2=0 \\ & \sin x=2 \text { has no solution } \end{aligned}\) \(\therefore \sin x=1\) has one solution which is…
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