KVPY Sample Paper KVPY Stream-SX Model Paper-4

\[\text{sin }47{}^\circ +\text{sin }61{}^\circ -\text{sin }11{}^\circ -\text{sin }25{}^\circ \] is equal to-

A) \[\sin \,36{}^\circ \]

B) \[\text{cos }36{}^\circ \]

C) \[\sin \,7{}^\circ \]

D) \[\text{cos }7{}^\circ \]

Correct Answer: D

Solution :

[D]

The given expression is equal to \[(\sin 47{}^\circ +\sin 61{}^\circ )-(\sin 11{}^\circ +\sin 25{}^\circ )\]

\[=2\sin 54{}^\circ cos7{}^\circ -2sin18{}^\circ \cos 7{}^\circ \]

\[=2\cos 7{}^\circ (\sin 54{}^\circ -\sin 18{}^\circ )\]

\[=2\cos 7{}^\circ \left[ \frac{\sqrt{5}+1}{4}-\frac{\sqrt{5}-1}{4} \right]=\cos 7{}^\circ .\]