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Introduction to Trigonometry · Class 10 · CBSE Mathematics

If sec theta + tan theta = x, then the value of sec theta - tan theta in terms of x is:

Practice question from Introduction to Trigonometry (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-9F7621

If sec⁡θ+tan⁡θ=x\sec \theta + \tan \theta = x, then the value of sec⁡θ−tan⁡θ\sec \theta - \tan \theta in terms of xx is:

  1. A.xx
  2. B.1x\frac{1}{x}Correct answer
  3. C.x2x^2
  4. D.1−x1 - x

Solution

We know the fundamental identity sec⁡2θ−tan⁡2θ=1\sec^2 \theta - \tan^2 \theta = 1. Factoring this gives (sec⁡θ+tan⁡θ)(sec⁡θ−tan⁡θ)=1(\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1. Substituting the given value, x(sec⁡θ−tan⁡θ)=1x(\sec \theta - \tan \theta) = 1, which means sec⁡θ−tan⁡θ=1x\sec \theta - \tan \theta = \frac{1}{x}.

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