Question

Prove that:cos 135º – cos 120°cos 135° + cos 120°= 3-2√2.​

Answer 1

(co135°-cos 120°)/(cos135°+cos120°)=3–2.2^1/2.

L.H.S.

cos135° =cos (180°-45°)= -cos 45° = -1/2^1/2.

cos120°=cos(180°-60°)= -cos60° = -1/2

=( -1/2^1/2 +1/2)/(-1/2^1/2 - 1/2)

=(1/2^1/2–1/2)/(1/2^1/2+1/2).

=(2^1/2 -1)/(2^1/2+1) , multiply above and below by (2^1/2 -1).

=(2^1/2–1)×(2^1/2–1)/(2^1/2+1)×(2^1/2–1).

=(2+1–2×2^1/2×1)/(2–1)

=(3- 2.2^1/2) , proved.

.....I hope this will help you