Question

th value of expression (sin80 - cos80) is negative ?

Answer 1

SinA-SinB =2 Sin(A+B/2)Cos(A-B/2). SinA=Cos(90-A)
=> Sin80-Cos80=> Sin80-Cos(90-10)=> Sin80-Sin10 =>2Sin(80+10/2)Cos(80-10/2)=>2Sin45Cos35 =>
2/√2Cos35=√2Cos35. As Cos function is positive So Sin80-Cos80 is not negative and a positive quantity.