Question

Please send help this is homework , and I wasn’t here to class I need help thank you

Answer 1

Solution

Step 1:

Apply double angle theorem.

$\begin{gathered} cos\left(\alpha+\beta\right)\text{ = cos}\alpha cos\beta\text{ - sin}\alpha sin\beta \\ cos(\alpha-\beta)=cos\text{\alpha cos\beta{\text{{\text{+s}}}\imaginaryI\text{{\text{n}}}}\alpha s}\imaginaryI\text{n\beta} \\ sin(\alpha+\beta)=sin\text{\alpha cos\beta{\text{{\text{+s}}}\imaginaryI\text{{\text{n}}}}}\beta cos\alpha \\ s\imaginaryI n(\alpha-\beta)=s\imaginaryI n\text{\alpha cos\beta-sin}\beta cos\alpha \end{gathered}$

Step 2:

Write the expression and substitute the values.

$\frac{cos\left(\alpha-\beta\right)-cos\left(\alpha+\beta\right)}{sin\left(\alpha-\beta\right)-sin\left(\alpha+\beta\right)}$

Step 3:

$\begin{gathered} \frac{cos\text{\alpha cos}\beta\text{+sin}\alpha s\imaginaryI\text{n\beta-\lparen cos}\alpha cos\beta-sin\alpha sin\beta\text{\rparen}}{s\imaginaryI n\text{\alpha cos\beta- s}\imaginaryI\text{n}\beta cos\alpha-\left(sin\alpha cos\beta+sin\beta cos\alpha\right)} \\ \frac{cos\text{\alpha cos}\beta+\text{s}\imaginaryI\text{n}\alpha s\imaginaryI\text{n\beta-cos}\alpha cos\beta+s\imaginaryI n\alpha s\imaginaryI n\beta}{s\imaginaryI n\text{\alpha cos\beta- s}\imaginaryI\text{n}\beta cos\alpha-s\imaginaryI n\alpha cos\beta-s\imaginaryI n\beta cos\alpha} \\ \frac{2sin\alpha sin\beta}{-2sin\beta cos\alpha} \\ -tan\alpha \end{gathered}$