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Hi! I was absent today and did not understand this lesson please I will be really grateful if you help me ! I appreciate it this is classwork assignment does not count as a test, I did the first question and it was right but the second one I do not know how to solve it

Hi I Was Absent Today And Did Not Understand This Lesson Please I Will Be Really Grateful If You Help Me I Appreciate It This Is Classwork Assignment Does Not C class=

Sagot :

Answer:

sin(α + β) = -84/205

tan(α + β) = 84/187

Explanation:

To find sin(α + β), we will use the following identity

[tex]\begin{gathered} \sin ^2\theta+\cos ^2\theta=1 \\ \text{Then} \\ \sin ^2(\alpha+\beta)^{}+\cos ^2(\alpha+\beta)^{}=1 \end{gathered}[/tex]

So, solving for sin(α + β), we get:

[tex]\sin (\alpha+\beta)=\pm_{}\sqrt[]{1-\cos^2(\alpha+\beta)}[/tex]

Now, we can replace cos(α + β) = -187/205 to get:

[tex]\begin{gathered} \sin (\alpha+\beta)=\pm\sqrt[]{1-(\frac{187}{205})^2} \\ \sin (\alpha+\beta)=\pm\frac{84}{205} \end{gathered}[/tex]

Then, α + β is on quadrant III. It means that the sine of the angle is negative. Therefore

sin(α + β) = -84/205

Finally, to add tan(α + β), we will use the following

[tex]\tan (\alpha+\beta)=\frac{\sin (\alpha+\beta)}{cos(\alpha+\beta)}[/tex]

Replacing the values, we get:

[tex]\tan (\alpha+\beta)=\frac{-\frac{84}{205}}{-\frac{187}{205}}=\frac{-84\times205}{205\times(-187)}=\frac{84}{187}[/tex]

Therefore

tan(α + β) = 84/187

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