Question
Evaluate the following:
$\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ$
$\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ$
✓
Answer
We find: $\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ$Since $\sin(90^\circ-\theta)=\cos\theta$ and $\cos(90^\circ-\theta)=\sin\theta$
$\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ$ $=\sin(90^\circ-55^\circ)\sin55^\circ-\cos(90^\circ-55^\circ)\cos55^\circ$ $=\cos55^\circ\sin55^\circ-\sin55^\circ\cos55^\circ$ $=1-1$$=0$
So value of $\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ\text{ is }0$
$\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ$ $=\sin(90^\circ-55^\circ)\sin55^\circ-\cos(90^\circ-55^\circ)\cos55^\circ$ $=\cos55^\circ\sin55^\circ-\sin55^\circ\cos55^\circ$ $=1-1$$=0$
So value of $\sin35^\circ\sin55^\circ-\cos35^\circ\cos55^\circ\text{ is }0$
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