Answer:
Explanation:
sin18° cos24°- cos12° sin6°/ sin24° sin6° + cos36° cos6° = tan12°
We can write the numerator and denominator of the left hand side of the equation as follows:
sin18° cos24°- cos12° sin6° = sin(18° + 24°) = sin42°
sin24° sin6° + cos36° cos6° = sin(24° + 6°) = sin30°
Therefore, the given equation can be written as:
sin42°/sin30° = tan12°
Since sin42° = 2sin21°cos21° and sin30° = 1/2, we can write the equation as:
2*sin21°*cos21°/(1/2) = tan12°
Simplifying the right hand side, we get:
4*sin21°*cos21° = 2*tan12°
Therefore, the given equation is:
tan12° = 2*sin21°*cos21°