Question

find the value of cos(270°+theta) cos(90°+theta) -sin(270°-theta) cos theta ​

Answer 1

sin( 270−Θ)=sin[180+(90−Θ)]

But we know that sin(180 + Θ)=−sinΘ)

∴ sin [ 180 + ( 90 - Θ)]=−sin(90−Θ)

But sin (90 -Θ)=cosΘ)

∴ sin(270−Θ)=−cosΘ−−−−−−−−−−−−−−−−−−

2) cos( 270−Θ)=cos[180+(90−Θ)]

But we know that cos(180 + Θ)=−cosΘ)

∴ cos [ 180 + ( 90 - Θ)]=−cos(90−Θ)

But cos (90 -Θ)=sinΘ)

∴ cos(270−Θ)=−sinΘ−−−−−−−−−−−−−−−−−−

3) tan( 270−Θ)=tan[180+(90−Θ)]

But we know that tan(180 + Θ)=tanΘ)

∴ tan[ 180 + ( 90 -Θ)]=tan(90−Θ)

But tan (90 -Θ)=cotΘ)

∴ tan(270−Θ)=cotΘ−−−−−−−−−−−−−−−−−

4) csc(270−Θ)=1sin(270+Θ)

But sin(270−Θ)=−cosΘ

∴ csc( 270−Θ)=1−cosΘ

∴ csc(270−Θ)=−secΘ−−−−−−−−−−−−−−−−−−

5) sec(270−Θ)=1cos(270+Θ)

But cos(270−Θ)=−sinΘ

∴ sec( 270−Θ)=−1sinΘ

∴ sec(270−Θ)=−cscΘ−−−−−−−−−−−−−−−−−−

6) cot(270−Θ)=1sin(270−Θ)

But tan(270−Θ)=cotΘ

∴ csc( 270−Θ)=1−cosΘ

∴ cot(270−Θ)=tanΘ−−−−−−−−−−−−−−−−−

these are all 270 degree ratios needed by u .