Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Combine the opposite terms in <math><mstyle displaystyle="true"><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>⋅</mo><mn>1</mn><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>⋅</mo><mn>1</mn></mstyle></math> .

Reorder the factors in the terms <math><mstyle displaystyle="true"><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>⋅</mo><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn><mo>⋅</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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