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NDA 2022 Maths · Mathematics · Trigonometric Functions and Identities · medium

If sec θ+tan θ=2, then sec θ equals

Single correct option

If sec⁡θ+tan⁡θ=2\sec\theta+\tan\theta=2, then sec⁡θ\sec\theta equals
  1. A. 34\dfrac34
  2. B. 53\dfrac53
  3. C. 54\dfrac54
  4. D. 32\dfrac{3}{2}
Show answer and solution

Answer: (C) 54\dfrac54

Since sec⁡2θ−tan⁡2θ=1\sec^2\theta-\tan^2\theta=1, we get sec⁡θ−tan⁡θ=12\sec\theta-\tan\theta=\frac12. Adding the two relations, 2sec⁡θ=522\sec\theta=\frac52, so sec⁡θ=54\sec\theta=\frac54. The value 34\frac34 is tan⁡θ\tan\theta.
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