Saved Bookmarks
| 1. |
If sec theta + tan theta =p ,then find the value of cosec theta |
|
Answer» SecA+tanA=p ----------------------------(1)∵, sec²A-tan²A=1.......(secA+tanA)(secA-tanA)=1......... secA-tanA=1/p -----------------------(2)Subtracting (2) from (1) we get,2tanA=p-1/p......, tanA=(p²-1)/2p.....cotA=2p/(p²-1)Now, cosec²A-cot²A=1.......cosec²A=1+cot²A...... cosec²A=1+{2p/(p²-1)}²....... cosec²A=1+4p²/(p²-1)²..,..cosec²A=(p⁴-2p²+1+4p²)/(p²-1)²......cosec²A=(p⁴+2p²+1)/(p²-1)².............., cosec²A=(p²+1)²/(p²-1)²...... cosecA=(p²+1)/(p²-1) (P²+1)/(p²-1) (p²+1)/(p²-1) Ans. |
|