Darcy gave her nail technician a $5.10 tip. The tip was 15% of the cost of the manicure. Write an equation to find b, the cos
1 answer:
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From the double-angle identity,
we can rewritte our given equation as:
By factoring 2cosx on the left hand side, we have
This equation has 2 solutions when
From equation (A), we obtain
and from equation (B), we have
On the other hand, we can find one more solution from the original equation by substituting x=0, that is,
then, x=0 is another solution. In summary, we have obtained the following solutions:
However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:
Therefore, the solution set is: {0}
