Prove that

(i)


(ii)


(iii)


(iv)


(v)


(i)sin80°cos20° - cos80°sin20° = sin(80° - 20°)

(using sin(A - B) = sinAcosB - cosAsinB)


= sin60°



(ii)cos45°cos15° - sin45°sin15° = cos(45° + 15°)


(using cos(A + B) = cosAcosB - sinAsinB)


= cos60°



(iii)cos75°cos15° + sin75°sin15° = cos(75° - 15°)


(using cos(A - B) = cosAcosB + sinAsinB)


= cos60°



(iv)sin40°cos20° + cos40°sin20° = sin(40° + 20°)


(using sin(A + B) = sinAcosB + cosAsinB)


= sin60°



(v)cos130°cos40° + sin130°sin40° = cos(130° - 40°)


(using cos(A - B) = cosAcosB + sinAsinB)


= cos90°


= 0


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