How do you find the exact value of $sin 60 cos 20 - cos 60 sin 20$ $sin60cos20-cos60sin20$ using the sum and difference, double angle or half angle formulas?

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Answer 1 · 2017-03-24T09:13:05

${sin 60}^{\circ} {cos 20}^{\circ} - {cos 60}^{\circ} {sin 20}^{\circ} = 0.6428$ $sin60^@cos20^@-cos60^@sin20^@=0.6428$

We use here the difference formula $sin A cos B - cos A sin B = sin (A - B)$ $sinAcosB-cosAsinB=sin(A-B)$

let $A = 60^{\circ}$ $A=60^@$ and $B = 20^{\circ}$ $B=20^@$

then using the formula

${sin 60}^{\circ} {cos 20}^{\circ} - {cos 60}^{\circ} {sin 20}^{\circ}$ $sin60^@cos20^@-cos60^@sin20^@$

= $sin (60^{\circ} - 20^{\circ})$ $sin(60^@-20^@)$

= ${sin 40}^{\circ}$ $sin40^@$

= $0.6428$ $0.6428$

How do you find the exact value of sin60cos20−cos60sin20sin60cos20-cos60sin20 using the sum and difference, double angle or half angle formulas?