Simplify 1/(sec(x)^2)+1/(csc(x)^2)

Problem

1/sec2(x)+1/csc2(x)

Solution

1. Apply reciprocal identities to rewrite the terms in terms of sine and cosine.

2. Substitute cos2(x) for 1/sec2(x) and sin2(x) for 1/csc2(x)

1/sec2(x)=cos2(x)

1/csc2(x)=sin2(x)

3. Combine the terms into a single expression.

cos2(x)+sin2(x)

4. Apply the Pythagorean identity which states that sin2(x)+cos2(x)=1

cos2(x)+sin2(x)=1

Final Answer

1/sec2(x)+1/csc2(x)=1

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