Question

What is the reciprocal of $cot\theta$?

• A. $cos\theta$
• B. $sin\theta$
• C. $tan\theta$
• D. $cosec\theta$

Answer 1

The correct option is C $tan\theta$

Reciprocal of $cot\theta =\frac{1}{cot\theta }$-------(i)

But, $cot\theta =\frac{cos\theta }{sin\theta }$.
Subatituting this in (i), we get,
Reciprocal of $cot\theta =\frac{1}{\frac{cos\theta }{sin\theta }}=\frac{sin\theta }{cos\theta }=tan\theta$
$(\because tan\theta =\frac{sin\theta }{cos\theta })$

Hence, reciprocal of $cot\theta$ is $tan\theta$.