| What is \[\text{cosec (75}{}^\circ \text{+}\theta \text{)}-\sec \,\,(15{}^\circ -\theta )\] \[-\tan \,\,(55{}^\circ +\theta )+\cot \,\,(35{}^\circ -\theta )\] |
A) \[-\,\,1\]
B) 0
C) 1
D) 3/2
Correct Answer: B
Solution :
| \[\text{cosec}\,\,(75{}^\circ +\theta )-\sec \,\,(15{}^\circ -\theta )\] |
| \[-\tan \,\,(55{}^\circ +\theta )+\cot \,\,(35{}^\circ -\theta )\] |
| \[\Rightarrow \]\[\text{cosec}\,\,(75{}^\circ +\theta )-\text{cosec}\,\,[90{}^\circ -(15{}^\circ -\theta )]\] |
| \[-\tan \,\,(55{}^\circ +\theta )+\tan \,\,[90{}^\circ -\,\,(35{}^\circ -\theta )]\] |
| \[\Rightarrow \]\[\text{cosec}\,\,(75{}^\circ +\theta )-\text{cosec}\,\,(75{}^\circ +\theta )\] |
| \[-\tan \,\,(55{}^\circ +\theta )+\tan \,\,(55{}^\circ +\theta )=0\] |
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