Question

find the value of sin 75

Answer 1

sin75

=sin (30+45)

= sin30cos45 + cos30sin45

=(1/2)(1/√2) + (√3/2)(1/√2)

=1/2√2 + √3/2√2

=(1+√3)/2√2

Answer 2

Hey there ! :))

We know that,

$sin 30 = \frac{1}{2} \\ sin45 = \frac{1}{ \sqrt{2} }$

Now,

sin75 = sin ( 30 + 45 )

= sin30 cos45 + sin45 cos30

$= \frac{1}{2} \times \frac{1}{\sqrt2} + \frac{1}{\sqrt2} \times \frac{\sqrt3}{2} \:$

$= \frac{1}{2 \sqrt 2} + \frac{ \sqrt3}{2 \sqrt 2} \:$

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


$\therefore sin 75 = \frac{ \sqrt{3} + 1}{2 \sqrt{2} }$

Hope helped!