SOLUTION: 1. If theta is an angle in quadrant 1, represent sin theta interms of cos theta 2. Find an equivalent expression: sec theta-sin theta tan theta 3. Solve 2 tan ^2 theta=-3sec thet

Algebra ->  Trigonometry-basics -> SOLUTION: 1. If theta is an angle in quadrant 1, represent sin theta interms of cos theta 2. Find an equivalent expression: sec theta-sin theta tan theta 3. Solve 2 tan ^2 theta=-3sec thet      Log On


   

Question 928575: 1. If theta is an angle in quadrant 1, represent sin theta interms of cos theta
2. Find an equivalent expression: sec theta-sin theta tan theta
3. Solve 2 tan ^2 theta=-3sec theta
4. Evaluate 2 cot (arc tan1)
Answer by lwsshak3(11628) About Me  (Show Source):
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1. If theta is an angle in quadrant 1, represent sin theta interms of cos theta
2. Find an equivalent expression: sec theta-sin theta tan theta
3. Solve 2 tan ^2 theta=-3sec theta
4. Evaluate 2 cot (arc tan1)
***
1. sinx=cos(90-x)
..
2.
..
3.2tan%5E2%28x%29=-3secx
2%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29=-3%281%2Fcosx%29
%282sin%5E2%28x%29%2Fcos%5E2%28x%29%29=-3%2Fcosx%29
lcd:cos^2(x)
2sin%5E2%28x%29=-3cosx
2%281-cos%5E2%28x%29%29=-3cosx
2-2cos%5E2%28x%29=-3cosx
2cos^2(x)-3cosx-2=0
(2cosx+1)(cosx-2)=0
cosx-2=0
cosx=2 (no solution, (1 ≤ cosx ≤ 1))
or
2cosx+1=0
cosx=-1/2
x=5π/6
..
4. 2 cot (arc tan1)=2cot(π/4)=2*1=2