Question

Prove that, cos 20+ cos 140– sin 10= 0

Answer 1

To prove that cos20 + cos140 - sin10 = 0

cos 20 + cos140 - sin10

We know that cos A + cos B = 2cos ($\frac{A+B}{2}$)cos ($\frac{A-B}{2}$)

so by applying formula where A = 20 and B = 140

2 cos ($\frac{140+20}{2}$) cos ($\frac{20-140}{2}$) - sin10

2 cos80.cos60 - sin10

We know cos60 = 1/2

cos80 - sin10

We know cos(90-x) = sinx

cos80 - cos(90-10)

cos80- cos80

0

Hence proved.