Simplify cos(theta)^2(1+tan(theta)^2)

Problem

cos2(θ)*(1+tan2(θ))

Solution

1. Identify the trigonometric identity for the expression inside the parentheses.

2. Apply the identity 1+tan2(θ)=sec2(θ) to substitute into the expression.

cos2(θ)*sec2(θ)

3. Use the reciprocal identity sec(θ)=1/cos(θ) to rewrite the secant term.

cos2(θ)1/cos2(θ)

4. Simplify the expression by canceling the common factors.

1

Final Answer

cos2(θ)*(1+tan2(θ))=1

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