Question

sin300°cosec1050°-tan(-120°)

Answer 1

Sin 300° cosec 1050°- tan (-120°)
Sin (360°-60°) cosec(1080°-30°)+tan(180°-60°)
(-sin60°)(-cosec30°)+tan(60°)
-1.732/2*2-(1.732)-3.464

Answer 2

Sin300=sin(2π-60)=sin(-60)
=-sin60°
Cosec1050=1/sin1050
=1/sin(6π-30)=-1/sin30°
Tan(-120)=-tan120=-tan(90+30)
=-(-tan30)=tan30°
So,
Sin300°cosec1050°-tan(-120°)
=-Sin60°*(-1/sin30°)-tan30°
=sin60°/sin30°-tan30°
Now,
sin60/sin30=sin(2*30)/sin30
=(2sin30°.cos30°)/sin30°
=2cos30°
sin60°/sin30°-tan30°
=2cos30-tan30
=(2*√3/2)-1/√3
=√3-1/√3
=(3-1)/√3
=2/√3
I hope it helps