Question

Prove that cos48.cos12 = 3 + (root5)/8

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

The given equation is:

$cos48{\times}cos12=\frac{3+\sqrt{5}}{8}$

Taking the LHS of the above equation, we get

$cos48{\times}cos12$

Multiplying and dividing by 2, we have

=$\frac{1}{2}(2cos48{\times}cos12)$

=$\frac{1}{2}(cos(48+12)+cos(48-12))$

=$\frac{1}{2}(cos60+cos36))$

=$\frac{1}{2}(\frac{1}{2}+\frac{\sqrt{5}+1}{4})$

=$\frac{1}{2}(\frac{2+\sqrt{5}+1}{4})$

=$\frac{3+\sqrt{5}}{8}$

=RHS

Hence proved.