Question

evaluate 8 by cot square theta minus 8 by cos square theta​

Answer 1

Step-by-step explanation:

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Answer 2

The value of $\dfrac{8}{\cot^2 A}-\dfrac{8}{\cos^2 A} =8\csc^2 A}$.

Step-by-step explanation:

We have,

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

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

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

Using the trigonometric identity,

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

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

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

Taking commonas $\dfrac{8}{\cos^2 A}$, we get

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

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

Using the trigonometric identity,

$\cos^2 A=1-\sin^2 A$

$=\dfrac{8}{\cos^2 A}(\dfrac{\cos^2 A}{\sin^2 A})$

$=\dfrac{8}{\sin^2 A}$

$=8\csc^2 A}$

Thus, the value of $\dfrac{8}{\cot^2 A}-\dfrac{8}{\cos^2 A} =8\csc^2 A}$.