Verifying Trig Identities

[bobbyflay21]

Verfify the following trig idenity:


1/(1-sin?) + 1/(1+sin?) = 2sec^2?

 

[galactus]

\(\displaystyle \frac{1}{1-sin(x)}+\frac{1}{1+sin(x)}\)

Cross multiply like you would when adding fractions, simplify, and it'll fall into place.

 

[bobbyflay21]

wouldn't that end up cancelling out the sin x? or do those two terms on the left also equal the 2 sec^2 x?

 

[galactus]

If you cross multiply:

\(\displaystyle \frac{1+sin(x)+1-sin(x)}{(1-sin(x))(1+sin(x))}\)

Yes, the sin's in the numerator cancel and you can then see why it is \(\displaystyle 2sec^{2}(x)\)

 

[bobbyflay21]

alright. thank you very much. do you happen to understand how to do my other posts? i am pretty desperate haha