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TS EAMCET · Maths · Trigonometric Equations

The equation that is satisfied by the general solution of the equation \(4-3 \cos ^2 \theta=5 \sin \theta \cos \theta\) is

  1. A \(7 \sin ^2 \theta+3 \cos ^2 \theta=4\)
  2. B \(\sin ^2 \theta-2 \cos \theta+\frac{1}{4}=0\)
  3. C \(\cot \theta-\tan \theta=\sec \theta\)
  4. D \(1+\sin ^2 \theta=3 \cos ^2 \theta\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(1+\sin ^2 \theta=3 \cos ^2 \theta\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Given that, } 4-3 \cos ^2 \theta=5 \sin \theta \cdot \cos \theta \\ & \therefore \quad\left(4-3 \cos ^2 \theta\right)^2=25 \sin ^2 \theta \cdot \cos ^2 \theta \\ & \Rightarrow 16+9 \cos ^4 \theta-24 \cos ^2 \theta=25\left(1-\cos ^2 \theta\right) \cos ^2…