Question

Second method of seca + tana=p then find coseca

Answer 1

SecA+tanA=p ----------------------------(1)
∵, sec²A-tan²A=1
or, (secA+tanA)(secA-tanA)=1
or, secA-tanA=1/p -----------------------(2)
Subtracting (2) from (1) we get,
2tanA=p-1/p
or, tanA=(p²-1)/2p
∴, cotA=2p/(p²-1)
Now, cosec²A-cot²A=1
or, cosec²A=1+cot²A
or, cosec²A=1+{2p/(p²-1)}²
or, cosec²A=1+4p²/(p²-1)²
or, cosec²A=(p⁴-2p²+1+4p²)/(p²-1)²
or, cosec²A=(p⁴+2p²+1)/(p²-1)²
or, cosec²A=(p²+1)²/(p²-1)²
or, cosecA=(p²+1)/(p