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The value of sin 75 $°$ = ____

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Detailed Solution

sin 75

°

= sin (45

°

+ 30

°

)
We know that
sin (

α

β

) = sin

α

cos

β

+ cos

α

sin

β

∴

sin 75

°

= sin (45

°

+ 30

°

)
= sin 45

°

cos 30

°

+ cos 45

°

sin 30

°

\frac{1}{\sqrt{2}}

\frac{\sqrt{3}}{2}

\frac{1}{\sqrt{2}} . \frac{1}{2}

\frac{\sqrt{3}}{2 \sqrt{2}}

\frac{1}{2 \sqrt{2}}

\frac{\sqrt{3} + 1}{2 \sqrt{2}}

Hence, the value of sin 75

°

\frac{\sqrt{3} + 1}{2 \sqrt{2}}

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