SOLUTION: Hi! Simplify: {{{ (1-2sin^2(x))/(cos^2(x))+tan^2(x) }}} Would be nice to have explanations too. Thanks

Algebra ->  Trigonometry-basics -> SOLUTION: Hi! Simplify: {{{ (1-2sin^2(x))/(cos^2(x))+tan^2(x) }}} Would be nice to have explanations too. Thanks      Log On


   

Question 730240: Hi!
Simplify:
+%281-2sin%5E2%28x%29%29%2F%28cos%5E2%28x%29%29%2Btan%5E2%28x%29+
Would be nice to have explanations too.
Thanks
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
tan%5E2%28x%29+=+sin%5E2%28x%29%2Fcos%5E2%28x%29


sin%5E2%28x%29+%2B+cos%5E2%28x%29=1 so cos%5E2%28x%29+=+1-sin%5E2%28x%29


So the expression becomes


They have the same denominator, so now add them.


Look at the denominators: 1-2%2Asin%5E2%28x%29+%2B+sin%5E2%28x%29+=+1-sin%5E2%28x%29


That goes over the common denominator: %281-sin%5E2%28x%29%29%2F%281-sin%5E2%28x%29%29+=+1