Question

prove that sin 20+ cos 50 = cos 10​

Answer 1

Using the following identity: sin(x)=cos(90-x)

sin(20)=cos(90-20) => sin(20)=cos(70)

So sin(20)+cos(50) becomes cos(70)+cos(50)

Using the following identity: cos(a)+cos(b)=2cos[(a+b)/2]cos[(a-b)/2]

cos(70)+cos(50)=2cos[(70+50)/2]cos[(70-50)/2]=2cos(60)cos(10)

cos(60)=1/2 so

2cos(60)cos(10)=2*1/2cos(10)=cos(10)