Question

secA+TanA =p then find the value of cosecA ​

Answer 1

Step-by-step explanation:

secA+tanA=p ----------- (i) ‘.'

sec²A-tan²A=1 (secA+tanA)(secA-tanA)=1 secA-tanA = 1/p ------------- (ii)

Subtracting eqn ii from I

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= (p²)² - 2p²- 1- 4p²/(p²-1)² cosec²A= (p²)² + 2p²+1/(p²-1)² cosec²A= (p²+1)² / (p²-1)² cosecA= (p²+1)/p²-1)