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

Problem

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

Solution

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

2. Apply the identity 1+tan(x)=sec(x) to rewrite the expression.

cos(x)*sec(x)

3. Use the definition of the secant function, which is the reciprocal of the cosine function.

sec(x)=1/cos(x)

4. Substitute the reciprocal identity into the expression.

cos(x)⋅1/cos(x)

5. Simplify the expression by canceling the common terms.

1

Final Answer

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

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