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Chapter 7: Q. 4 (page 500)

find the exact value of the expression
sin 75 $°$ + sin 15 $°$

Short Answer

Expert verified

sin75 $°$ +sin15 $° = 1.2247448714$

Step by step solution

01

Step 1. Rewriting the expression

sin(x)+sin(y)=2 $\sin (\frac{x + y}{2}) \cos (\frac{x - y}{2})$
localid="1646417268045" $\sin 75 ° + \sin 15 ° = 2 \sin (\frac{75 ° + 15 °}{2}) \cos (\frac{75 ° - 15 °}{2}) = 2 \sin 45 ° \cos 30 °$

02

Step 2. Calculations

Now our expression becomes $2 \sin 45 ° \cos 30 ° = 2 \frac{1}{\sqrt{2}} \frac{\sqrt{3}}{2} = \sqrt{\frac{3}{2}} = 1.2247448714$

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Most popular questions from this chapter

Establish each identity.

$\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$

$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$ .

Establish each identity.

$\tan θ + c o t θ = s e c θ c s c θ$

Establish each identity.

$\frac{\sin θ + \cos θ}{\cos θ} - \frac{\sin θ - \cos θ}{\sin θ} = s e c θ c s c θ$

In Problems 9–36, find the exact value of each expression.

$\sin (\cos^{- 1} \frac{1}{2})$

See all solutions

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