Simplify sin(x)sec(x)+cos(x)csc(x)

Problem

sin(x)*sec(x)+cos(x)*csc(x)

Solution

1. Rewrite the reciprocal functions sec(x) and csc(x) in terms of sin(x) and cos(x)

sec(x)=1/cos(x)

csc(x)=1/sin(x)

2. Substitute these expressions back into the original equation.

sin(x)⋅1/cos(x)+cos(x)⋅1/sin(x)

3. Express the terms as fractions.

sin(x)/cos(x)+cos(x)/sin(x)

4. Apply the quotient identities tan(x)=sin(x)/cos(x) and cot(x)=cos(x)/sin(x)

tan(x)+cot(x)

Final Answer

sin(x)*sec(x)+cos(x)*csc(x)=tan(x)+cot(x)

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