Question #ded10

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Answer 1 · 2017-01-21T04:01:04

$(sin(pi + theta )+ cos( pi/2+theta) + cot( pi- theta))/tan((3pi)/2-theta)$

$=(-sin( theta )-sin( theta) -cot( theta))/cot(theta)$

$=(-2sin( theta) -cot( theta))/cot(theta)$

$=-2sin( theta)/cottheta -cot( theta)/cot(theta)$

$=-2sin( theta)/(costheta/sintheta) -1$

$=-2sin^2( theta)/costheta-1$

$=-(2(1-cos^2 theta))/costheta-1$

$=-2/costheta+(2cos^2theta)/costheta-1$

$=-2sectheta+2costheta-1$

$=2costheta-2sectheta-1$