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# Trigonometric Identities ( Trig Identities )

1. 1
Prove:
$$\tan x\cos x = \sin x$$ ( Using Trig Identities )
2. 2
Prove:
$$\sin x \left(\frac{\cos x}{\tan x}\right)= \cos^2 x$$
3. 3
Prove:
$$\cos x= \left(\frac{\sin x}{\tan x}\right)$$
4. 4
Prove:
$$\frac{1}{\sin^2 x}+ \frac{1}{\cos^2 x}= \frac{1}{\sin^2 x \: \cos^2 x}$$
5. 5
Prove:
$$\tan x + \cot x= \frac{1}{\sin x \: \cos x}$$
6. 6
Prove:
$$\csc x- \sin x= \cos x \cot x$$
7. 7
Prove:
$$\frac{1}{\csc^2 x}= \frac{\tan^2 x}{1+\tan^2 x}$$
8. 8
Prove:
$$\frac{1}{1-\sin x}+\frac{1}{1+\sin x}=2\sec^2 x$$
9. 9
Prove:
$$\frac{\sin^2 x}{1-\cos x}=1+\cos x$$
10. 10
Prove:
$$\cos^2 x-\sin^2 x=2\cos^2 x-1$$
11. 11
Prove:
$$\cos^2 x+\sin^2 x+\tan^2 x=\sec^2 x$$
12. 12
Prove:
$$\tan^2 x-\sin^2 x=\sin^2 x \: \tan^2 x$$
13. 13
Prove:
$$(\cos x+\sin x)^2=1+2\sin x \: \cos x$$
14. 14
Prove:
$$\frac{1+2\sin x \: \cos x}{\sin x+\cos x}=\sin x+\cos x$$
15. 15
Prove:
$$(1+\tan^2 x)(1-\cos^2 x)=\tan^2 x$$
16. 16
Prove:
$$\frac{\cos x}{1-\sin x}=\frac{1+\sin x}{\cos x}$$

Tough question !
17. 17
Prove:
$$\csc x+\cot x=\frac{\sin x}{1-\cos x}$$

Another tough question - similar to previous video
18. 18
Prove:
$$\tan x=\frac{1+\sin x-\cos^2 x}{\cos x+\cos x\sin x}$$

( trigonometry / trig )

$$e=mc^2$$