(i) sin80°cos20° - cos80°sin20° = sin(80° - 20°)
(using sin(A - B) = sinAcosB - cosAsinB)
= sin60°
= \(\frac{\sqrt{3}}2{}\)
(ii) cos45°cos15° - sin45°sin15° = cos(45° + 15°)
(Using cos(A + B) = cosAcosB - sinAsinB)
= cos60°
= \(\frac{1}{2}\)
(iii) cos75°cos15° + sin75°sin15° = cos(75° - 15°)
(using cos(A - B) = cosAcosB + sinAsinB)
= cos60°
= \(\frac{1}{2}\)
(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
