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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

If 3 θ=4 θ , then what is the value of (45^ ^ +.θ) ?

If 3cos⁡θ=4sin⁡θ3 \cos \theta=4 \sin \theta, then what is the value of tan⁡(45∘+θ)\tan \left(45^{{}^{\circ}}+\right.\theta) ?

Options

  1. A1010
  2. B77
  3. C72\frac{7}{2}
  4. D74\frac{7}{4}

Correct answer

B. 77

Step-by-step solution

3cos⁡θ=4sin⁡θ⇒sin⁡θcos⁡θ=34⇒tan⁡θ=34\begin{aligned} & 3 \cos \theta=4 \sin \theta \\ & \Rightarrow \frac{\sin \theta}{\cos \theta}=\frac{3}{4} \Rightarrow \tan \theta=\frac{3}{4}\end{aligned}\therefore \tan (45+\theta)=\frac{\tan 45^{{}^{\circ}}+\tan \theta}{1-\tan 45^{{}^{\circ}} \cdot \tan \theta}=\frac{1+\frac{3}{4}}{1-\frac{3}{4}}=\frac{7}{1}=7$
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