Introduction to Trigonometry
CH08 Question Bank
CBSE_CH08_QUESTION_BANK
Grade 10
Question:
Show that $(1-\cos^2\theta)\,\text{cosec}^2\theta = 1$.
Step-by-Step Solution
Key Concept: Use the identity $1-\cos^2\theta=\sin^2\theta$, then simplify with the reciprocal relation.
$1-\cos^2\theta=\sin^2\theta$ (Pythagorean identity). [1.0 Mark]
$\sin^2\theta\times\text{cosec}^2\theta=\sin^2\theta\times\dfrac{1}{\sin^2\theta}=1$. Hence shown. [1.0 Mark]
Correct Answer:
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