Replace <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>-</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> with an equivalent expression <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>-</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> using the fundamental identities.

Use the difference formula for sine to simplify the expression. The formula states that <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><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> .

Remove parentheses.

Simplify each term.

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

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

Convert from <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mrow></mfrac></mstyle></math> to <math><mstyle displaystyle="true"><mi>sec</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Do you know how to Expand Using Sum/Difference Formulas csc(pi/2-theta)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.