Answer :
sin75
=sin (30+45)
= sin30cos45 + cos30sin45
=(1/2)(1/√2) + (√3/2)(1/√2)
=1/2√2 + √3/2√2
=(1+√3)/2√2
Hey there ! :))
We know that,
[tex]sin 30 = \frac{1}{2} \\ sin45 = \frac{1}{ \sqrt{2} } [/tex]
Now,
sin75 = sin ( 30 + 45 )
= sin30 cos45 + sin45 cos30
[tex]= \frac{1}{2} \times \frac{1}{\sqrt2} + \frac{1}{\sqrt2} \times \frac{\sqrt3}{2} \: [/tex]
[tex]= \frac{1}{2 \sqrt 2} + \frac{ \sqrt3}{2 \sqrt 2} \: [/tex]
[tex] = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } [/tex]
[tex] \therefore sin 75 = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } [/tex]
Hope helped!
We know that,
[tex]sin 30 = \frac{1}{2} \\ sin45 = \frac{1}{ \sqrt{2} } [/tex]
Now,
sin75 = sin ( 30 + 45 )
= sin30 cos45 + sin45 cos30
[tex]= \frac{1}{2} \times \frac{1}{\sqrt2} + \frac{1}{\sqrt2} \times \frac{\sqrt3}{2} \: [/tex]
[tex]= \frac{1}{2 \sqrt 2} + \frac{ \sqrt3}{2 \sqrt 2} \: [/tex]
[tex] = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } [/tex]
[tex] \therefore sin 75 = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } [/tex]
Hope helped!