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)
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1. sinx=cos(90-x)
..
2. {{{secx-sinxtanx
=(1/cosx)-(sinx(sinx/cosx))=(1-(sin^2(x)))/(cosx)=(cos^2(x))/cosx=cosx}}}
..
3.{{{2tan^2(x)=-3secx}}}
{{{2(sin^2(x)/cos^2(x))=-3(1/cosx)}}}
{{{(2sin^2(x)/cos^2(x))=-3/cosx)}}}
lcd:cos^2(x)
{{{2sin^2(x)=-3cosx}}}
{{{2(1-cos^2(x))=-3cosx}}}
{{{2-2cos^2(x)=-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