Question

prove that 4(cos 66 deg + sin 84 deg) = root 3 + root 15

Answer 1

Answer:

Step-by-step explanation:

LHS = 4(cos 66 deg + sin 84 deg)

=4(cos 66° + cos 6°)

= 4 × 2 cos((66°+6°)/2) cos((66°-6°)/2)   [∵ cosA + cosB  = 2 cos((A+B)/2) cos((A-B)/2)]

= 8 cos(36°) cos(30°)  

=>  If we take cos36° = (√5 +1) / 4, then

= 8 × (√5 +1)/4 × (√3/2)

= (√5 +1) × (√3)

=   √3* √5 + √3

= √15 + √3

= √3 + √15 = RHS

Thus, LHS = RHS.

=> So the given equation 4(cos 66 deg + sin 84 deg) = root 3 + root 15, is said to be in equality.