Question

If secQ+tanQ=p, then find the value of cosec Q

Answer 1

Answer:

cosec Q = ( p² + 1 )/ ( p² - 1 )

Step-by-step explanation:

1 / cos Q  +  sin Q / cos Q = p

( 1 + sin Q ) / cos Q = p

1 + sin Q = p cos Q

1 + sin Q = p √( 1 - sin² Q )

p = ( 1 + sin Q )/√( 1 - sin² Q )    /²

p² = ( 1 + sin Q )² / ( 1 - sin Q ) ( 1 + sin Q ).    After cancelling 1 + sin Q :

p² = ( 1 + sin Q ) / ( 1 - sin Q )

1 + sin Q = p² - p² sin Q

sin Q ( p² + 1 ) = p² - 1

sin Q = ( p² - 1 ) / ( p² + 1 )

cosec Q = 1 / sin Q = ( p² + 1 ) / ( p² - 1 )

Answer 2

Answer:

(p²+1)/(p²-1)

Step-by-step explanation:

Given secФ + tanФ = p, --(1)then

secФ - tanФ = 1/p,---(2) since (secФ + tanФ)(secФ - tanФ) = 1[property]

Adding (1) and (2), we get

secФ = (p + 1/p)/2

Subtracting (1)-(2), we get

tanФ = (p - 1/p)/2

cosecФ = secФ/tanФ = (p+1/p)/(p-1/p)

=(p²+1)/(p²-1).