SOLUTION: I'm a little lost, I don't know how to approach this problem. It says, Find the acute angle theta that satisfies the equation tan theta = cot(theta + 45degrees)

Algebra ->  Trigonometry-basics -> SOLUTION: I'm a little lost, I don't know how to approach this problem. It says, Find the acute angle theta that satisfies the equation tan theta = cot(theta + 45degrees)      Log On


   

Question 879281: I'm a little lost, I don't know how to approach this problem. It says,
Find the acute angle theta that satisfies the equation tan theta = cot(theta + 45degrees)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the acute angle theta that satisfies the equation tan theta = cot(theta + 45degrees)
cot(x+45)
tan%28x%2B45%29=%28tanx%2Btan45%29%2F%281-tanx%2Atan45%29=%28tanx%2B1%29%2F%281-tanx%29
cot%28x%2B45%29=1%2F%28tan%28x%2B45%29%29=%281-tanx%29%2F%28tanx%2B1%29
tanx=cot%28x%2B45%29=%281-tanx%29%2F%28tanx%2B1%29
tan%5E2%28x%29%2Btan%28x%29=1-tan%28x%29
tan%5E2%28x%29%2B2tan%28x%29-1=0
solve for tan(x) by quadratic formula:
tan%28x%29+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=2, c=-1
ans:
tan(x)=-2.4142 (reject, not an acute angle)
or
tan(x)=0.4142
x≈22.5˚