SarkariPYQ

SSC CPO 2022 PYQ — Question 135

SSC CPO - 9 Nov 2022 - Shift 2 • Quantitative Aptitude • Q135

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Simplify.

sin⁡8θcos⁡θ−sin⁡6θcos⁡3θcos⁡2θcos⁡θ−sin⁡3θsin⁡4θ\rm \frac{\sin 8\theta \cos \theta - \sin 6\theta \cos 3\theta}{ \cos 2\theta \cos \theta - \sin 3\theta \sin 4\theta}

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. tan2θ.

sin⁡8θcos⁡θ−sin⁡6θcos⁡3θcos⁡2θcos⁡θ−sin⁡3θsin⁡4θ\rm \frac{\sin 8\theta \cos \theta - \sin 6\theta \cos 3\theta}{ \cos 2\theta \cos \theta - \sin 3\theta \sin 4\theta}

⇒ 2sin⁡8θcos⁡θ−2sin⁡6θcos⁡3θ2cos⁡2θcos⁡θ−2sin⁡3θsin⁡4θ\rm \frac{2\sin 8\theta \cos \theta - 2\sin 6\theta \cos 3\theta}{ 2\cos 2\theta \cos \theta - 2\sin 3\theta \sin 4\theta}

⇒ sin9θ+sin7θ−(sin9θ+sin3θ)cos⁡3θ+cos⁡θ−(cos⁡θ−cos7θ)\rm \frac{sin9\theta + sin7\theta - (sin9\theta+sin3\theta)}{ \cos 3\theta + \cos \theta - (\cos \theta - cos7\theta)}

⇒ sin7θ−sin3θcos⁡3θ+cos⁡7θ\rm \frac{sin7\theta - sin3\theta }{ \cos 3\theta + \cos 7\theta }

⇒​​​​​​​ 2sin5θsin⁡2θ2cos⁡5θcos⁡2θ\rm \frac{2sin5\theta \sin2\theta }{ 2\cos 5\theta \cos 2\theta } = tan2θ