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Sin18° cos24°- cos12° sin6°/ sin24° sin6° + cos36° cos6° = tan12°​

User Vborutenko
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1 Answer

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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°

User Bcleary
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