Question

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

Answer 1

Answer:

Step-by-step explanation:

8/$cos^{2}$θ - 8/cot²θ

= 8(1/cos²θ - 1/cot²θ) , taking 8 as a common element

=8(sec²θ - tan²θ) , since 1/cosθ=secθ

                                  and 1/cotθ= tanθ

=8×1 , since sec²θ - tan²θ=1

=8

Answer 2

The value of $\dfrac{8}{\cos^2 \theta} -\dfrac{8}{\cot^2 \theta}$ = 8

Step-by-step explanation:

We have,

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

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

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

= $8\sec^2 \theta -\dfrac{8}{\cot^2 \theta}$

Using the trigonometric identity,

$\sec A=\dfrac{1}{\cos A}$

= $8\sec^2 \theta -8\tan^2 \theta$

Using the trigonometric identity,

$\tan A=\dfrac{1}{\cot A}$

= $8(\sec^2 \theta -8\tan^2 \theta)$

Using the trigonometric identity,

$\sec^2 A -\tan^2 A=1$

= 8 × 1

= 8

∴ The value of $\dfrac{8}{\cos^2 \theta} -\dfrac{8}{\cot^2 \theta}$ = 8