SOLUTION: Find the number of solutions and find the solution of equation Tan(x) + Sec(x) = 2Cos(x) where x lies in the interval [0, π]?

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Question 1184289: Find the number of solutions and find the solution of equation Tan(x) + Sec(x) = 2Cos(x) where x lies in the interval [0, π]?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Tan%28x%29+%2B+Sec%28x%29+=+2Cos%28x%29 <===> Sin%28x%29%2FCos%28x%29+%2B+1%2FCos%28x%29+=+2Cos%28x%29

===> Sin%28x%29+%2B+1+=+2Cos%5E2%28x%29+=+2+-+2Sin%5E2%28x%29 ===> 2Sin%5E2%28x%29+%2B+Sin%28x%29-1=0

<===> %282Sin%28x%29+-+1+%29%28Sin%28x%29+%2B+1+%29+=+0

===> Sin(x) = 1/2 or Sin(x) = -1

===> x+=+highlight%28pi%2F6%29 or x+=+highlight%28%285pi%29%2F6%29 or x+=+cross%28%283pi%29%2F2%29