Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
If $\sec\theta + \tan\theta = x$, show that $\sec\theta - \tan\theta = \dfrac{1}{x}$.
Step-by-Step Solution
Key Concept: Multiply $(\sec\theta+\tan\theta)$ by $(\sec\theta-\tan\theta)$ and use the identity $\sec^2\theta-\tan^2\theta=1$.
$(\sec\theta+\tan\theta)(\sec\theta-\tan\theta)=\sec^2\theta-\tan^2\theta=1$ (standard identity). [1.5 Marks]
Given $\sec\theta+\tan\theta=x$, substituting: $x(\sec\theta-\tan\theta)=1$. [1.0 Mark]
$\sec\theta-\tan\theta=\dfrac{1}{x}$. Hence shown. [0.5 Mark]
Correct Answer:
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