Start on the right side.

Apply pythagorean identity.

Now consider the left side of the equation.

Write <math><mstyle displaystyle="true"><mi>cot</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> in sines and cosines using the quotient identity.

Apply the reciprocal identity to <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Because the two sides have been shown to be equivalent, the equation is an identity.

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