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