Verify the Identity 13sec(x)sin(x)=13cot(x)tan(x)^2

Problem

13*sec(x)*sin(x)=13*cot(x)*tan2(x)

Solution

1. Identify the goal to transform the left-hand side (LHS) to match the right-hand side (RHS).

2. Rewrite the LHS using the reciprocal identity sec(x)=1/cos(x)

LHS=13⋅1/cos(x)⋅sin(x)

3. Simplify the expression using the quotient identity sin(x)/cos(x)=tan(x)

LHS=13*tan(x)

4. Rewrite the RHS using the quotient identities cot(x)=1/tan(x)

RHS=13⋅1/tan(x)⋅tan2(x)

5. Simplify the RHS by canceling one factor of tan(x)

RHS=13*tan(x)

6. Compare the simplified results of both sides to confirm they are equal.

13*tan(x)=13*tan(x)

Final Answer

13*sec(x)*sin(x)=13*cot(x)*tan2(x)

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