Simplify cos(x)^2+cos(x)^2tan(x)^2

Problem

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

Solution

1. Factor out the common term cos^2(x) from both terms in the expression.

cos^2(x)*(1+tan^2(x))

2. Identify the Pythagorean identity for the expression inside the parentheses.

1+tan^2(x)=sec^2(x)

3. Substitute the identity back into the expression.

cos^2(x)*sec^2(x)

4. Apply the reciprocal identity sec(x)=1/cos(x)

cos^2(x)⋅1/cos^2(x)

5. Simplify the product by canceling the common terms.

1

Final Answer

cos^2(x)+cos^2(x)*tan^2(x)=1

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