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NDA 2025
Exam
NDA
Year
2025
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2025 · Mathematics · Trigonometric Ratios & Identities

Consider the following for the two (02) items that follow: Let 2 α...

Consider the following for the two (02) items that follow:
Let 2sin⁡α+cos⁡α=22\sin\alpha + \cos\alpha = 2, where 0<α<90°0 < \alpha < 90°.

What is tan⁡α\tan\alpha equal to?

Options

  1. A12\dfrac{1}{2}
  2. B11
  3. C34\dfrac{3}{4}
  4. D22

Correct answer

C. 34\dfrac{3}{4}

Step-by-step solution

Given 2sin⁡α+cos⁡α=22\sin\alpha + \cos\alpha = 2

Dividing both sides by cos⁡α\cos\alpha, we get:

2tan⁡α+1=2sec⁡α2\tan\alpha + 1 = 2\sec\alpha

Squaring both sides:

(2tan⁡α+1)2=4sec⁡2α(2\tan\alpha + 1)^2 = 4\sec^2\alpha

4tan⁡2α+4tan⁡α+1=4(1+tan⁡2α)4\tan^2\alpha + 4\tan\alpha + 1 = 4(1 + \tan^2\alpha)

4tan⁡2α+4tan⁡α+1=4+4tan⁡2α4\tan^2\alpha + 4\tan\alpha + 1 = 4 + 4\tan^2\alpha

4tan⁡α=34\tan\alpha = 3

tan⁡α=34\tan\alpha = \dfrac{3}{4}

Answer: 34\dfrac{3}{4}
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