prove that cos^2x+tan^2xcos^2x=1

**skeske1234** · March 30th 2009, 07:09 AM

can you explain all steps please because:
I did it and I got down to LS:
(1-sin^2x)/sin^2x
so the answer on the left side would be 0,
but I dont think that is right, where would my error be?

**Mush** · March 30th 2009, 07:43 AM

Originally Posted by skeske1234

can you explain all steps please because:
I did it and I got down to LS:
(1-sin^2x)/sin^2x
so the answer on the left side would be 0,
but I dont think that is right, where would my error be?

$\tan^2(x) = \frac{\sin^2(x)}{\cos^2(x)}$

Hence:

$\cos^2(x) \tan^2(x) = \cos^2(x)\frac{\sin^2(x)}{\cos^2(x)}= \sin^2(x)$

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