Question

sin290°.tan100°cos780°÷cot370°sin1125°.cos200°​

Answer 1

it is given that

sin290°. tan100°. cos780°/(cot370°. sin1125°. cos200°)

we know, sin290° = sin(270° + 20°) = -cos20°

tan100° = tan(90° + 10°) = -cot10°

cos780° = cos(720° + 60°) = cos60°

cot370° = cot(360° + 10°) = cot10°

sin1125° = sin(1080° + 45°) = sin45°

cos200° = cos(180° + 20°) = -cos20°

sin290°. tan100°. cos780°/(cot370°. sin1125°. cos200°)

= (-cos20°).(-cot10°)(cos60°)/{(cot10°)(sin45°).(-cos20°)}

= -cos60°/sin45°

= -(1/2)/(1/√2)

= -1/√2

therefore, value of given expression is -1/√2

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Answer 2

tan100° =tan (90°+10°)=-cot10

cos780°=cos(720+60°)=cos60°

cot370°=cot(360°+10°)=cot10°

sin1125°=sin(1080°+45°)=sin45°

cos200°=cos(180°+20°)=-cos20°

sin290°. tan100°. cos780°/(cot370°. sin1125°. cos200°

=(-cos20°). (-cot10°)(cos60°)/{(cot10°)(sin45°). (-cos20°)}

= -cos60°/sin45°

= -(1/2)/(1/√2)

= -1/√2

So, the value of given expression is -1/√2