A) \[-1\]
B) 1
C) 0
D) none of these
Correct Answer: B
Solution :
| Note that \[\cos 158{}^\circ =\cos \,(180{}^\circ -22{}^\circ )=-cos22{}^\circ \] |
| & \[\cos 98{}^\circ =\cos \,(90{}^\circ +8{}^\circ )=-\sin 8{}^\circ \] |
| Also \[\cos 157{}^\circ =\cos \,(180{}^\circ -23{}^\circ )=-cos23{}^\circ \] |
| & \[\cos 97{}^\circ =\cos \,(90{}^\circ +7{}^\circ )=-sin7{}^\circ \] |
| \[\therefore \] Given expression \[=\frac{\sin 22{}^\circ \cos 8{}^\circ +\cos 22{}^\circ \sin 8{}^\circ }{\sin 23{}^\circ \cos 7{}^\circ +\cos 23{}^\circ \sin 7{}^\circ }\] |
| \[=\frac{(\sin 22{}^\circ +8{}^\circ )}{(\sin 23{}^\circ +7{}^\circ )}=1\] \[\therefore \] Ans. is B |
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