Question

sin 24+sin 32+sin 204+sin 212=​

Answer 1

Sin25° + sin32° +sin204° +sin212° = ?

= sin25° + sin32° +sin (180 + 24 ) + Sin ( 180° + 32°)

= Sin25° + sin32° + sin24° + 2Sin32 = 0

Answer 2

The value of $sin 24^{\circ} + sin 32^{\circ} + sin 204^{\circ} + sin 212^{\circ}$ is 0.

Step-by-step explanation:

Given,

$sin 24^{\circ} + sin 32^{\circ} + sin 204^{\circ} + sin 212^{\circ}$

We can also write this equation in this form,

=  $sin 24^{\circ} + sin 32^{\circ} + sin (180^{\circ} +24^{\circ}) + sin (180^{\circ} + 32^{\circ})$

=  $sin 24^{\circ} + sin 32^{\circ} - sin 24^{\circ} - sin32^{\circ}$              $[ sin (180^{\circ} +\theta) = - sin \theta ]$

= $0$

So, the value of $sin 24^{\circ} + sin 32^{\circ} + sin 204^{\circ} + sin 212^{\circ}$ is 0.

Trigonometry property we used,

$sin \theta = sin (180^{\circ} -\theta)$

Learn more about trigonometry formulas -

https://brainly.in/question/4068827?msp_srt_exp=6

More about trigonometry -

https://brainly.in/question/42022714?msp_srt_exp=6

#SPJ3