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

Problem

tan2(x)−tan2(x)*sin2(x)

Solution

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

2. Factor out the common term tan2(x) from the expression.

tan2(x)*(1−sin2(x))

3. Apply the Pythagorean identity sin2(x)+cos2(x)=1 which implies 1−sin2(x)=cos2(x)

tan2(x)*cos2(x)

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

(sin(x)/cos(x))2*cos2(x)

5. Simplify the expression by squaring the fraction and canceling the common cos2(x) terms.

sin2(x)/cos2(x)*cos2(x)

sin2(x)

Final Answer

tan2(x)−tan2(x)*sin2(x)=sin2(x)

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