Question

hey guys.............

Here is my question................

Prove that


Cos12° + cos60° +cos84° = cos24° + cos48°

And and and

One more question

Value of cos34°

PLZZ answer it quickly

Answer 1

1) prove that
cos 12° + cos 60° + cos 84° = cos 24° + cos 48°

solution:
LHS = cos12° + (cos84° + cos60°)
LHS= cos12° + (cos(72°+12°) + cos (72°-12°))
LHS= cos12° + 2cos72° cos12°
[note: cos(A+B) + cos(A-B) = 2 cosA cosB]
LHS= cos12°(1+2cos72°)
LHS= cos12°(1+2sin18°)
[note: cos(90-A) = sinA]
LHS= cos12°(1+2((√5-1)/4))
[note: sin18° = (√5-1)/4]
LHS= cos12°((2+√5-1)/2)
LHS= cos12° ((1+√5)/2)

RHS= cos24° + cos48°
RHS= cos(36°-12°) + cos(36°+12°)
[note: cos(A+B) + cos(A-B) = 2 cosA cosB]
RHS= 2cos36° cos12°
[note: cos36° = (√5+1)/4]
RHS= 2((√5+1)/4) cos12°
RHS= cos12°((1+√5)/2)

therefore LHS = RHS
hence proved

value of cos36° = (√5+1)/4