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NDA 2023 Maths · Mathematics · Trigonometric Functions and Identities · easy

If tan θ=3/4 and θ lies in the third quadrant, then sin θ+cos θ equals

Single correct option

If tan⁡θ=34\tan\theta=\dfrac34 and θ\theta lies in the third quadrant, then sin⁡θ+cos⁡θ\sin\theta+\cos\theta equals
  1. A. −75-\dfrac75
  2. B. 75\dfrac75
  3. C. −15-\dfrac15
  4. D. 15\dfrac15
Show answer and solution

Answer: (A) −75-\dfrac75

A right triangle with legs 3,43,4 has hypotenuse 55. In the third quadrant both sine and cosine are negative, so sin⁡θ=−35\sin\theta=-\tfrac35 and cos⁡θ=−45\cos\theta=-\tfrac45. The sum is −75-\tfrac75. Option 75\tfrac75 ignores the quadrant, and ±15\pm\tfrac15 comes from mixing the signs.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake