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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NTA Abhyas 2020 · Mathematics · Trigonometric Ratios & Identities

The value of 2 ^ 2 θ + 4 (θ + α)sin α sin θ + 2 ( α + θ ) is

The value of 2sin⁡2θ+4cos⁡(θ+α)sinαsinθ+cos⁡2(α+θ)2\sin^{2} \theta + 4\cos \left(\theta + \alpha\right)sin \alpha sin \theta + \cos 2 ( \alpha + \theta ) is

Options

  1. Acosθ+cosαcos \theta + cos \alpha
  2. Bindependent of θ\theta
  3. Cindependent of α\alpha
  4. Dindependent of both θ\theta and α\alpha

Correct answer

B. independent of θ\theta

Step-by-step solution

2\sin^{2} \theta + 2\cos \left(\theta + \alpha\right)\left(\cos \left(\theta - \alpha\right) - \cos \left(\theta + \alpha\right)\right) +\left(2\cos^{2} \left(\theta + \alpha\right) -1\right)<br/><br/><br /><br />= 2\sin^{2} θ++2(cos⁡2θ−sin⁡2α)−1\theta ++2\left(\cos^{2} \theta - \sin^{2} \alpha\right) -1

=2−2sin⁡2α−1=cos⁡2α−sin⁡2α= 2 - 2\sin^{2} \alpha -1 = \cos^{2} \alpha - \sin^{2} \alpha
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