# Thread: how to start/ simplify these trigonometric functions

1. ## how to start/ simplify these trigonometric functions

csc A - sin A to cos A cot A

and

sin A cot^2 A (sec - 1) to sin A

2. Originally Posted by xahjika
csc A - sin A to cos A cot A

and

sin A cot^2 A (sec - 1) to sin A
$\csc(A) - \sin(A) = \frac{1}{\sin(A)} - \sin(A)$

$= \frac{1}{\sin(A)} - \frac{\sin^2(A)}{\sin(A)}$

$= \frac{\cos^2{A}}{\sin(A)} = \frac{\cos(A) \times \cos(A)}{\sin(A)}$

$= \frac{\cos(A)}{\sin(A)} \times \cos(A)$

3. Are you sure you've written the second one out properly?

4. Originally Posted by Mush
Are you sure you've written the second one out properly?
oops sorry

sin (A) cot^2 (A) (sec^2 (A) - 1) to sin (A)

5. Originally Posted by xahjika
oops sorry

sin (A) cot^2 (A) (sec^2 (A) - 1) to sin (A)
Consider the identity:

$\sin^2(A) + \cos^2(A) = 1$

Divide it by $\cos^2(A)$

$\tan^2(A) + 1 = \sec^2(A)$

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

$\sin(A) \cot^2(A) \tan^2(A)$
And you know that $\tan^2(A) = \frac{1}{\cot^2(A)}$