Question : If $0^{\circ} < θ < 90^{\circ}$ and $2 \sin^{2} θ + 3 \cos θ = 3$ , then the value of $θ$ is:
Option 1: 30°
Option 2: 60°
Option 3: 45°
Option 4: 75°

Question

Question : If $\sin (θ + 18^{\circ}) = \cos 60^{\circ} (0 < θ < 90^{\circ})$ , then the value of $\cos 5 θ$ is:

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Answer 1

Correct Answer: 60°

Solution : We know that $\sin^{2} θ + \cos^{2} θ = 1$
Using the value of $\sin^{2} θ$ in the equation, we get,
⇒ $2 (1 - \cos^{2} θ) + 3 \cos θ = 3$
⇒ $2 - 2 \cos^{2} θ + 3 \cos θ = 3$
⇒ $2 \cos^{2} θ - 3 \cos θ + 1 = 0$
⇒ $2 \cos^{2} θ - 2 \cos θ - \cos θ + 1 = 0$
⇒ $(2 \cos θ - 1) (\cos θ - 1) = 0$
⇒ $\cos θ = \frac{1}{2}$ or $\cos θ = 1$
Since $0^{\circ} < θ < 90^{\circ}$ ,
So, $\cos θ = \frac{1}{2} = \cos 60^{\circ}$
$∴ θ = 60^{\circ}$
Hence, the correct answer is 60°.

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Question : If 0∘<θ<90∘ and 2sin2⁡θ+3cos⁡θ=3, then the value of θ is:Option 1: 30°Option 2: 60°Option 3: 45°Option 4: 75°

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Question : If $0^{\circ} < θ < 90^{\circ}$ and $2 \sin^{2} θ + 3 \cos θ = 3$ , then the value of $θ$ is:
Option 1: 30°
Option 2: 60°
Option 3: 45°
Option 4: 75°