Prove that: cos 7π/12 + cos π/12 = sin 5π/12 – sin π/12

Evaluate the following:

(i) sin 78⁰ cos 18⁰ – cos 78⁰ sin 18⁰ (ii) cos 47⁰ cos 13⁰ - sin 47⁰ sin 13⁰

(iii) sin 36⁰ cos 9⁰ + cos 36⁰ sin 9⁰ (iv) cos 80⁰ cos 20⁰ + sin 80⁰ sin 20⁰

If cosA = –12/13 and cotB = 24/7, where A lies in the second quadrant and B in the third quadrant, find the values of the following:

(i) sin(A +B) (ii) cos(A +B) (iii) tan(A +B)

Prove that:

Prove that:

(i) ⁽ii)

(ii)