Question

secA + tanA =p find value of cosecA​

Answer 1

Answer:

secA + tanA =p find value of cosecA

Step-by-step explanatio

Answers

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)/(p²-1)

Answer 2

Answer:

Step-by-step explanation:

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)/(p²-1)