Question

. If sin(x + y)=sin x.cos y+cos x.sin y, then find the value of sin 75 degrees​

Answer 1

`\sf (√(6)+√(2))/(4)`

Explanation:

Trigonometry:

75 = 45 + 30

Sin (x + y) = Sin x *Cos y + Cos x * Sin y

Sin (45 + 30) = Sin 45 * Cos 30 + Cos 45 * Sin 30

`\sf =(1)/(√(2))*(√(3))/(2)+(1)/(√(2))* (1)/(2)\\\\\\=(√(3))/(2√(2))+(1)/(2√(2))\\\\\\=(√(3)*√(2))/(2*√(2)*√(2))+(1*√(2))/(2√(2)*√(2))\\\\\\=(√(6))/(2*2)+(√(2))/(2*2)\\\\\\=(√(6)+√(2))/(4)`