Evaluate the following: (i) sin 78 0 cos 18 0 – cos 78 0 sin 18 0 (ii) cos 47 0 cos 13 0 - sin 47 0 sin 13 0 (iii) sin 36 0 cos 9 0 + cos 36 0 sin 9 0 (iv) cos 80 0 cos 20 0 + sin 80 0 sin 20 0

Question

Philoid · Accepted Answer

(i) Given sin 78⁰ cos 18⁰ – cos 78⁰ sin 18⁰

We know that sin(A -B) = sinA cosB - cosA sinB

⇒ sin 78⁰ cos 18⁰ – cos 78⁰ sin 18⁰ = sin(78 – 18) °

= sin 60°

(ii) Given cos 47⁰ cos 13⁰ - sin 47⁰ sin 13⁰

We know that cosA cosB – sinA sinB = cos(A +B)

⇒ cos 47⁰ cos 13⁰ - sin 47⁰ sin 13⁰ = cos(47 + 13) °

= cos 60°

= 1/2

∴ cos 47⁰ cos 13⁰ - sin 47⁰ sin 13⁰ = 1/2

(iii) Given sin 36⁰ cos 9⁰ + cos 36⁰ sin 9⁰

We know that sin(A +B) = sinA cosB + cosA sinB

⇒ sin 36⁰ cos 9⁰ + cos 36⁰ sin 9⁰ = sin(36 + 9) °

= sin 45°

(iv) Given cos 80⁰ cos 20⁰ + sin 80⁰ sin 20⁰

We know that cosA cosB + sinA sinB = cos(A -B)

⇒ cos 80⁰ cos 20⁰ + sin 80⁰ sin 20⁰ = cos(80 - 20) °

= cos 60°

= 1/2

∴ cos 80⁰ cos 20⁰ + sin 80⁰ sin 20⁰ = 1/2

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

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