Simplify tan(x)^2-tan(x)^2sin(x)^2

Problem

tan^2(x)−tan^2(x)*sin^2(x)

Solution

1. Identify the common factor in both terms of the expression.

2. Factor out the common term tan^2(x) from the expression.

tan^2(x)*(1−sin^2(x))

3. Apply the Pythagorean identity sin^2(x)+cos^2(x)=1 which implies 1−sin^2(x)=cos^2(x)

tan^2(x)*cos^2(x)

4. Substitute the definition of the tangent function, tan(x)=sin(x)/cos(x) into the expression.

(sin(x)/cos(x))^2*cos^2(x)

5. Simplify the expression by squaring the fraction and canceling the common cos^2(x) terms.

sin^2(x)/cos^2(x)*cos^2(x)

sin^2(x)

Final Answer

tan^2(x)−tan^2(x)*sin^2(x)=sin^2(x)

Want more problems? Check here!