SOLUTION: What is {{{tan(theta)}}} if {{{cos(pi+theta)=sin(theta)}}}?

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Question 1107874: What is tan%28theta%29 if cos%28pi%2Btheta%29=sin%28theta%29?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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If  cos%28pi%2Btheta%29 = sin%28theta%29  then

sin%28theta%29 = cos%28pi%29%2Acos%28theta%29+-+sin%28pi%29%2Asin%28theta%29 = %28-1%29%2Acos%28theta%29+-+0%2Asin%28theta%29 = -cos%28theta%29.


Thus,  if  {{cos(pi+theta)}}} = sin%28theta%29  then  sin%28theta%29 = -cos%28theta%29.


Hence,  if  cos%28pi%2Btheta%29 = sin%28theta%29,  then  tan%28theta%29 = sin%28theta%29%2Fcos%28theta%29 = -1.


It implies  theta = 5pi%2F4.

Solved.