Simplify tan(x)^2-3sin(x)tan(x)sec(x)

Problem

tan2(x)−3*sin(x)*tan(x)*sec(x)

Solution

1. Rewrite the expression using the definitions of tan(x) and sec(x) in terms of sin(x) and cos(x)

tan(x)=sin(x)/cos(x)

sec(x)=1/cos(x)

2. Substitute these definitions into the second term of the expression.

tan2(x)−3*sin(x)*(sin(x)/cos(x))*(1/cos(x))

3. Multiply the components of the second term.

tan2(x)−(3*sin2(x))/cos2(x)

4. Identify the trigonometric identity for tan2(x) in the second term.

sin2(x)/cos2(x)=tan2(x)

5. Combine the terms to simplify the expression.

tan2(x)−3*tan2(x)

−2*tan2(x)

Final Answer

tan2(x)−3*sin(x)*tan(x)*sec(x)=−2*tan2(x)

Want more problems? Check here!