Cos 1-cos 2-cos 3- -cos 179-

The correct option is A 0cos 1^∘ + cos 2^∘ + cos 3^∘ + .... + cos 179^∘ = (cos 1^∘ + cos 179^∘) + cos 2^∘ + cos 178^∘) + ... + (cos 89^∘ + cos 91^∘) + cos 90^∘ ...

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Byju's Answer

Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

cos 1∘+cos 2∘...

Question

$cos 1^{\circ} + cos 2^{\circ} + cos 3^{\circ} + . . . . + cos 179^{\circ}$ =

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Solution

$cos 1^{\circ} + cos 2^{\circ} + cos 3^{\circ} + . . . . + cos 179^{\circ}$
= $(cos 1^{\circ} + cos 179^{\circ}) + cos 2^{\circ} + cos 178^{\circ}) + . . . + (cos 89^{\circ} + cos 91^{\circ}) + cos 90^{\circ}$
= $(cos 1^{\circ} - cos 1^{\circ}) + (cos 2^{\circ} - cos 2^{\circ}) + . . . + (cos 89^{\circ} - cos 89^{\circ}) + cos 90^{\circ} = 0$

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Similar questions

cos 1^{\circ} + cos 2^{\circ} + cos 3^{\circ} + . . . . + cos 179^{\circ}

Q. The
value of

cos 1^{\circ} cos 2^{\circ} cos 3^{\circ} . . . . . cos 179^{\circ} is

Q. The value of

c o s 1^{\circ} \times c o s 2^{\circ} \times c o s 3^{\circ} \times . . . . . . . \times c o s 179^{\circ}

is:

c o s 1^{0} + c o s 2^{0} + c o s 3^{0} + . . . . . . . + c o s 179^{0} =

The value of $c o s 1^{\circ} c o s 2^{\circ} c o s 3^{\circ} . . . . c o s 179^{\circ}$ is

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cos1∘+cos2∘+cos3∘+....+cos179∘ =

cos1∘+cos2∘+cos3∘+....+cos179∘ = (cos1∘+cos179∘)+cos2∘+cos178∘)+...+(cos89∘+cos91∘)+cos90∘ = (cos1∘−cos1∘)+(cos2∘−cos2∘)+...+(cos89∘−cos89∘)+cos90∘=0

$cos 1^{\circ} + cos 2^{\circ} + cos 3^{\circ} + . . . . + cos 179^{\circ}$ =