The value of sin 1-sin 2-sin 359- is equal to

The correct option is A 0 nbsp; nbsp;sin 1^∘+sin 2^∘+ ⋯ +sin 359^∘ =sin 1^∘+sin 2^∘+ ⋯ +sin 179^∘+sin 180^∘ +sin 181^∘+sin 182^∘+⋯+sin 359^∘ nbsp; =si ...

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Byju's Answer

Standard XII

Mathematics

Principal Solution of Trigonometric Equation

The value of ...

Question

The value of $sin 1^{\circ} + sin 2^{\circ} + \dots + sin 359^{\circ}$ is equal to

0

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180

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Solution

The correct option is A $0$
$sin 1^{\circ} + sin 2^{\circ} + \dots + sin 359^{\circ}$
$= sin 1^{\circ} + sin 2^{\circ} + \dots + sin 179^{\circ} + sin 180^{\circ}$
$+ sin 181^{\circ} + sin 182^{\circ} + \dots + sin 359^{\circ}$
$= sin 1^{\circ} + sin 2^{\circ} + \dots + sin 179^{\circ} + sin 180^{\circ}$
$+ sin (180 + 1)^{\circ} + sin (180 + 2)^{\circ} + \dots + sin (180 + 179)^{\circ}$
$= sin 1^{\circ} + sin 2^{\circ} + \dots + sin 179^{\circ} + sin 180^{\circ}$
$- sin 1^{\circ} - sin 2^{\circ} - \dots - sin 179^{\circ}$ $[∵ sin (π + θ) = - sin θ]$
$= sin 180^{0}$
$= 0$ $[∵ sin 180^{0} = 0]$

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Similar questions

Q. The value of the

sin 1^{\circ} + sin 2^{\circ} + \dots \dots + sin 359^{\circ} + sin 360^{\circ}

is equal to

sin $1^{\circ}$ $\times$ sin $2^{\circ}$ $\times$ sin $3^{\circ}$ $\times$ …….. $\times$ sin $180^{\circ}$ is equal to:

sin 1^{\circ} sin 2^{\circ} sin 3^{\circ} . . . . . . sin 180^{\circ}

is equal to ____.

Q. The value of

log (sin 1^{0}) log (sin 2^{0}) . . . . . log (sin 179^{0})

Q. If

\frac{1}{sin 45^{\circ} sin 46^{\circ}} + \frac{1}{sin 47^{\circ} sin 48^{\circ}} + . . . + \frac{1}{sin 135^{\circ} sin 134^{\circ}} = \frac{1}{sin A^{\circ}}

and

\frac{1}{sin 1^{\circ} sin 2^{\circ}} + \frac{1}{sin 2^{\circ} sin 3^{\circ}} + . . . + \frac{1}{sin 89^{\circ} sin 90^{\circ}} = \frac{B}{sin 1^{\circ}},

then which of the following is/are correct ?

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The value of sin1∘+sin2∘+⋯+sin359∘ is equal to

The value of $sin 1^{\circ} + sin 2^{\circ} + \dots + sin 359^{\circ}$ is equal to