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COMEDK · Maths · 9. Trigonometric Equations

The number of solution of \(\cos ^2 x=3-3 \sin x\) \(\forall x \in[0,2 \pi]\) is

  1. A 0
  2. B 1
  3. C 2
  4. D 3
Verified Solution

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…