Let f(θ)=sin⁡(arctan⁡(sin⁡θcos⁡2θ))f(\theta) = \sin \left( \arctan \left( \frac{\sin \theta}{\sqrt{\cos 2\theta}} \right) \right)…

Mathematics

Problem

Let f(θ)=sin⁡(arctan⁡(sin⁡θcos⁡2θ))f(\theta) = \sin \left( \arctan \left( \frac{\sin \theta}{\sqrt{\cos 2\theta}} \right) \right), where −π4<θ<π4-\frac{\pi}{4} < \theta < \frac{\pi}{4}. Then, the value of dd(tan⁡θ)⋅f(θ)\frac{d}{d(\tan \theta)} \cdot f(\theta) is a. 1 b. 2 c. 3 d. 4

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