InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
30. If sec tane p, then find the value of coseco, |
|
Answer» Secθ+tanθ=p ----------------------(1)∵, sec²θ-tan²θ=1or, (secθ+tanθ)(secθ-tanθ)=1or, secθ-tanθ=1/p ----------------(2)Adding (1) and (2) we get,2secθ=p+1/por, secθ=(p²+1)/2p∴, cosθ=1/secθ=2p/(p²+1)∴, sinθ=√(1-cos²θ)=√[1-{2p/(p²+1)}²]=√[1-4p²/(p²+1)²]=√[{(p²+1)²-4p²}/(p²+1)²]=√[(p⁴+2p²+1-4p²)/(p²+1)²]=√(p⁴-2p²+1)/(p²+1)=√(p²-1)²/(p²+1)=(p²-1)/(p²+1)∴, cosecθ=1/sinθ=1/[(p²-1)/(p²+1)]=(p²+1)/(p²-1) |
|