| What is \[\sin 25{}^\circ \sin 35{}^\circ \sec 65{}^\circ \sec 55{}^\circ \]equal to? |
A) \[-\,\,1\]
B) \[0\]
C) \[\frac{1}{2}\]
D) \[1\]
Correct Answer: D
Solution :
| \[\sin 25{}^\circ \sin 35{}^\circ \sec 65{}^\circ \sec 55{}^\circ \] |
| \[=\sin 25{}^\circ \sin 35{}^\circ .\frac{1}{\cos 65{}^\circ }.\frac{1}{\cos 55{}^\circ }\] |
| \[=\sin 25{}^\circ .\sin 35{}^\circ \times \frac{1}{\cos \,\,(90{}^\circ -25{}^\circ )}\times \frac{1}{\cos \,\,(90{}^\circ -35{}^\circ )}\]\[=\sin 25{}^\circ \times \sin 35{}^\circ \times \frac{1}{\sin 25{}^\circ }\times \frac{1}{\sin 35{}^\circ }=1\] |
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