# How to prove the identity ? #1- (tan^2x/(1+tan^2x)) = cos^2x#

##### 3 Answers

Hence Proved !

#1+tan^2x = sec^2x# #1 - (tan^2x/sec^2x) = cos^2x# #tan^2x/sec^2x = sin^2x# #1 - sin^2x = cos^2x#

#### Explanation:

Line 1 is a common Pythagorean identity. Substituting gives line 2. Simplifying the complex fraction in 2 into sin and cos functions gives line 3. Line 4 is also a common Pythagorean identity.

Here is how I proved the identity:

#### Explanation:

To solve this, we will use a bunch of trigonometric identities.

First, we know that

We also know that

From these identities, we can rewrite the equation as:

We also know that

Let's rewrite the division part with

We know that dividing something is the same as multiplying it by the reciprocal, or

Since

And now the cleaned up version looks like this:

Finally, we know that

Hope this helps!