If cot θ=-3/4 on the interval (90°, 180°) find sin θ? If sin^2 θ * sec θ * cot θ = (sqrt3)/2 find sin(θ+pi)?

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Answer 1 · 2018-03-16T05:10:56

# 4/5, and -sqrt3/2#.

#cottheta=-3/4:.csc^2theta=1+cot^2theta=1+9/16=25/16#.

#rArr csc theta=+-5/4#.

But, for #theta in (90^@,180^@), sintheta > 0, csc theta > 0#.

#:. sintheta=1/csctheta=+4/5#.

Next, #sin^2theta*sectheta*cottheta=sqrt3/2#.

#rArr sin^2theta*1/costheta*costheta/sintheta=sqrt3/2#.

# rArr sintheta=sqrt3/2#.

#:."The Reqd. Value="sin(pi+theta)#,

#=-sintheta...[because, (pi+theta) in Q_3," where, "sintheta<0]#,

#=-sqrt3/2#.