Introduction to Trigonometry and Its Applications
NCERT Exemplar Ch 08
CBSE_NCERT_EXEMPLAR_CH08
Grade 10
Question:
If $\tan \theta + \cot \theta = 2$, then the value of $\tan^2 \theta + \cot^2 \theta$ is:
$1$
$2$
$4$
$0$
Step-by-Step Solution
Key Concept: Square both sides: $(\tan \theta + \cot \theta)^2 = 2^2$.
Stepwise Solution:
\tan^2 \theta + \cot^2 \theta + 2 \tan \theta \cot \theta = 4. [0.5 Mark]
Since $\tan \theta \cot \theta = 1$: $\tan^2 \theta + \cot^2 \theta + 2 = 4 \Rightarrow \tan^2 \theta + \cot^2 \theta = 2$. [0.5 Mark]
Marking Scheme:
• Squaring given relation: 0.5 Mark
• Evaluating $\tan^2 \theta + \cot^2 \theta = 2$: 0.5 Mark
Correct Answer: $2$
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