Verify the Identity sin(pi/2-x)tan(x)=sin(x)

Problem

sin(π/2−x)*tan(x)=sin(x)

Solution

1. Apply the cofunction identity to the first term on the left side of the equation.

sin(π/2−x)=cos(x)

2. Substitute the identity back into the expression.

cos(x)*tan(x)

3. Use the quotient identity to rewrite the tangent function in terms of sine and cosine.

tan(x)=sin(x)/cos(x)

4. Multiply the terms and simplify the expression by canceling the common factor.

cos(x)⋅sin(x)/cos(x)

5. Simplify the result to show it equals the right side of the identity.

sin(x)

Final Answer

sin(π/2−x)*tan(x)=sin(x)

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