SOLUTION: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi if possible. {{{cot^2(pi/2-(x))}}} = sec(x) + 1 Thanks!

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi if possible. {{{cot^2(pi/2-(x))}}} = sec(x) + 1 Thanks!       Log On


   

Question 1082998: Solve the equation for 0≤x≤2pi. Write your answer as a multiple of pi if possible.

cot%5E2%28pi%2F2-%28x%29%29 = sec(x) + 1

Thanks!
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

cot%5E2%28pi%2F2-%28x%29%29+=+sec%28x%29+%2B+1

Since pi%2F2-%28x%29 is the complement of x,

cot%28pi%2F2-%28x%29%29=tan%28x%29

tan%5E2%28x%29+=+sec%28x%29+%2B+1

Since 1%2Btan%5E2%28theta%29=sec%5E2%28theta%29, tan%5E2%28theta%29=sec%5E2%28theta%29-1 

sec%5E2%28x%29-1=sec%28x%29%2B1

sec%5E2%28x%29-sec%28x%29-2=0

%28sec%28x%29%5E%22%22-2%29%28sec%28x%29%5E%22%22%2B1%29=0

sec%28x%29-2=0,  sec%28x%29%2B1=0

sec%28x%29=2,  sec%28x%29=-1

For sec%28x%29=2 using the unit circle,

matrix%281%2C5%2C%0D%0A%0D%0Ax%2C%22%22=%22%22%2Cpi%2F3%2C+%22%2C%22%2C5pi%2F3%29

For sec%28x%29=-1 using the unit circle,

matrix%281%2C3%2Cx%2C%22%22=%22%22%2Cpi%29

Three solutions.

Edwin