Question

prove sin75*=[√6+2]/4

Answer 1

Sin(A+B) = SinACosB + CosASinB,

75° can be written as 45°+30°

Let A be 45° and B be 30° , You can take vice versa, As the result will be same,

=> Sin(45+30) = Sin45Cos30 + Cos45Sin30,
=>( 1/√2)(√3/2)+(1/√2)(1/2)
=> √3/(2√2) + 1/(2√2)
=> (√3+1)/(2√2)
Multiply 4 on both sides
=> √6+4/8√2
=>√6+2/4

Hope you understand,

Have a great day !