Question

Cosec squared theta minus cot square theta is equal to

Answer 1

Given: $cosec^2 \theta - cot^2 \theta$

To find: we have to find the value of $cosec^2 \theta - cot^2 \theta$

Solution:

Here we have the given equation

$cosec^2 \theta - cot^2 \theta = \dfrac{1}{sin^2 \theta} - \dfrac{cos^2 \theta}{sin^2 \theta} \\=\dfrac{1-cos^2 \theta}{sin^2 \theta}$

we know that $sin^2 \theta +cos^2 \theta =1$ we can also write it as $1-cos^2 \theta=sin^2 \theta$

$=\dfrac{sin^2 \theta}{sin^2 \theta}\\=1$

Hence the answer is 1

Answer 2

Given: $cosec^2\theta-cot^2\theta$

To find: we have to find the value of  $cosec^2\theta-cot^2\theta$

Solution:

Here we have the given equation

$cosec^2\theta-cot^2\theta=\frac{1}{sin^2\theta}-\frac{cos^2\theta}{sin^2\theta}$

$=\frac{1-cos^2\theta}{sin^2\theta}$

we know that $sin^2\theta+cos^2\theta=1$

we can also write it as $1-cos^2\theta=sin^2\theta$

$=\frac{sin^2\theta}{sin^2\theta}$

$=1$

Hence the answer is 1.