Question

Choose the correct option:
$(cosec\theta +cot\theta )\times (1-cos\theta )=$

• A. $cot\theta$
• B. $sec\theta$
• C. $sin\theta$
• D. $cosec\theta$

Answer 1

The correct option is C

$sin\theta$

$cosec\theta =\frac{1}{sin\theta },cot\theta =\frac{cos\theta }{sin\theta }$

When we rationalise $(1-cos\theta )$, we get,

$(\frac{1}{sin\theta }+\frac{cos\theta }{sin\theta })\times \frac{(1-cos\theta )\times (1+cos\theta )}{(1+cos\theta )}=\frac{(1+cos\theta )}{sin\theta }\times \frac{(1-co{s}^2\theta )}{(1+cos\theta )}$.
After simplifying we get $\frac{(1-co{s}^2\theta )}{sin\theta }$. Now $1-co{s}^2\theta =si{n}^2\theta$ on further simplifying,
$\Rightarrow \frac{si{n}^2\theta }{sin\theta }=sin\theta$