A) \[1\]
B) \[0\]
C) \[-\,\,1\]
D) \[\frac{1}{2}\]
Correct Answer: A
Solution :
\[\sin 20{}^\circ \cos 70{}^\circ +\cos 20{}^\circ \sin 70{}^\circ \] \[=\sin \,\,(90{}^\circ -70{}^\circ )\cdot \cos 70{}^\circ +\cos \,\,(90{}^\circ -70{}^\circ )\sin 70{}^\circ \] \[={{\cos }^{2}}70{}^\circ +{{\sin }^{2}}70{}^\circ \] \[=1\]\[[\because {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1]\]
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