Question

if sin(A+B) = sinA.cosB+cosA.sinB then find sin75

Answer 1

sin 75 = sin(30+45)=sin30.cos45+cos30.sin45
                               =1/(2*2^1/2)}+3^1/2*1/2*2^1/2}
                               =(1+3^1/2)/2

Answer 2

Answer:

sin75°

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

Explanation:

Value of sin75

= sin(45+30)

$\boxed {sin(A+B)\\=sinAcosB+cosAsinB}$

Here,

A = 45° , B = 30°

= sin45°cos30°+cos45°sin30°

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

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

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

Therefore,

sin75°

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

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