Apply the sum of angles identity.

Apply the difference of angles identity.

Combine the opposite terms in <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>+</mo><mi>cos</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>-</mo><mi>cos</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> .

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