SOLUTION: If cos54 = t, determine cos144 in terms of t

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Question 1057159: If cos54 = t, determine cos144 in terms of t
Answer by ikleyn(52852) About Me  (Show Source):
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If cos(54°) = t, determine cos(144°) in terms of t
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Notice that  144° = 90° + 54°.


Based on it, I will find cos(144°) in one steps.


cos(144°) = cos(90°+54°) =  ( apply the formula cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) ) = 

            cos(90°)*cos(54°) - sin(90°)*sin(54°) = 0%2At+-+1%2Asqrt%281-t%5E2%29 = -sqrt%281-t%5E2%29.

Solved.   The answer is   cos(144°) = -sqrt%281-t%5E2%29.