Question

Find the value of cos 570° sin 510° + sin (-330°) cos (-390°).

Answer 1

Step-by-step explanation:

$\begin{matrix} \cos { 570^{ 0 } } \cdot \sin { 510^{ 0 } } +\sin \left( { -{ { 33 }^{ 0 } } } \right) \cdot \cos \left( { -{ { 390 }^{ 0 } } } \right) \\ { { degree } }\, \, { { change } }\, \, \, { { into } }\, \, { { radius } } \\ \Rightarrow \cos \left( { \pi +{ { 30 }^{ 0 } } } \right) \cdot \sin \left( { 3\pi -{ { 30 }^{ 0 } } } \right) -\sin \left( { 2\pi -{ { 30 }^{ 0 } } } \right) \cos \left( { 2\pi +3 } \right) \\ \Rightarrow -\cos { 30^{ 0 } } \times \sin { 30^{ 0 } } +\sin { 30^{ 0 } } \times \cos { 30^{ 0 } } \\ \Rightarrow \frac { { -\sqrt { 3 } } }{ 2 } \times \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \times \frac { { \sqrt { 3 } } }{ 2 } =0\, \, \, \, \, \, \, Ans \\ \end{matrix}$

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Answer 2

$\huge \large \bold{Answer}$

$\small\mapsto \cos570°. \sin510° + \sin( - 330°)$

$\mapsto570° = 540° + 30° = 3\pi + \frac{\pi}{6}$

$\mapsto \cos(3\pi +\frac{ \pi}{6} ).\sin(3\pi - \frac{\pi}{6}) - \: \: \: \: \sin(2\pi - \frac{\pi}{6} ) \cos(2\pi + \frac{\pi}{6} ) - \cos \frac{\pi}{6} . \sin \frac{\pi}{6 } + \sin \frac{\pi}{6}. \cos \frac{\pi}{6} = 0$