Question

What is the value of sin(80°)cos(20°) – cos(80°)sin(20°)?

Answer 1

The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

What is difference formula in trignometry?

The difference formula in trignometry for the sine funciton is given as,

$\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)$

The trignometric equation given in the problem is,

$\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)$

Compare this equation with the above eqution, we get,

$A=80^o\\B=20^o$

Thus, this equation can be written as,

$\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}$

Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.

Learn more about the difference formula in trignometry here;

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