Question

evaluate 8 / cot2 theta _ 8 / cos2 theta​

Answer 1

Answer:

zero(0)

Step-by-step explanation:

8/cos2theta-8/cos2theta

=8-8/cos2theta

=0/cos2theta

=0

Answer 2

The value of $\dfrac{8}{\cot^2 \theta}-\dfrac{8}{\cos^2 \theta}$ is equal to - 8.

Step-by-step explanation:

We have,

$\dfrac{8}{\cot^2 \theta}-\dfrac{8}{\cos^2 \theta}$

To find, the value of $\dfrac{8}{\cot^2 \theta}-\dfrac{8}{\cos^2 \theta} = ?$

∴ $\dfrac{8}{\cot^2 \theta}-\dfrac{8}{\cos^2 \theta}$

$=\dfrac{8}{\dfrac{\cos^2 \theta}{\sin^2 \theta} }-\dfrac{8}{\cos^2 \theta}$

Using the trigonometric identity,

$\cot \theta}=\dfrac{\cos \theta}{\sin \theta}$

$=\dfrac{8\sin^2 \theta}{\cos^2 \theta}-\dfrac{8}{\cos^2 \theta}$

$= \dfrac{8}{\cos ^2 \theta} (\sin^2 \theta-1)$

$= \dfrac{8}{\cos ^2 \theta} (-\cos ^2 \theta)$

Using the trigonometric identity,

$\sin^2 \theta+\cos^2 \theta=1$

= - 8

Thus, the value of $\dfrac{8}{\cot^2 \theta}-\dfrac{8}{\cos^2 \theta}$ is equal to - 8.