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Ksenya-84 [330]
2 years ago
14

Please help i beg i never get these right

Mathematics
1 answer:
Anuta_ua [19.1K]2 years ago
3 0

Answer:

\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}

Step-by-step explanation:

Given

\sin(105^o)

Required

Solve

Using sine rule, we have:

\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)

This gives:

\sin(105^o) = \sin(60 + 45)

So, we have:

\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)

In radical forms, we have:

\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}

\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}

Take LCM

\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}

Rewrite as:

\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}

Hence:

\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}

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