SOLUTION: prove that tan t = sin 2t/1 + cos 2t and hence obtain the value of tan 15 and 45 and express the result in standard form

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Question 977115: prove that tan t = sin 2t/1 + cos 2t and hence obtain the value of tan 15 and 45 and express the result in standard form
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
LHS=
tan%28t%29=sin%28t%29%2Fcos%28t%29
=2%2Asin%28t%29cos%28t%29%2F%282%2Acos%5E2%28t%29%29 [Multiplying Num. and Den. by 2*cos(t)]
=sin%282t%29%2F%282%2Acos%5E2%28t%29-1%2B1%29
=sin%282t%29%2F%28cos%282t%29%2B1%29
=RHS
Hence,
tan15 = sin30/(1+cos30)
=%281%2F2%29%2F%281%2Bsqrt%283%29%2F2%29
=1%2F%282%2Bsqrt%283%29%29
Also,
tan45 = sin90/(1+cos90)
=1%2F%281%2B0%29
= 1