Question

If
$\sec( \alpha ) + \tan( \alpha ) = p$
then find the value of
$\cosec ( \alpha )$
No spam !!
​

Answer 1

Solution==>>

Given secA+tanA=p.......(1)

we know that sec²A-tan²A=1

(secA+tanA)(secA-tanA)=1

p×secA-tanA=1

secA-tanA=1/p......(2)

Add equation (1) and (2)

sec+-tanA+secA-tanA=p+1/p

2secA=p²+1/p

secA=p²+1/2p.....

we know that

cosA=1/secA=1/p²+1/2p

cosA=2p/p²+1

we also know that,

sin²A=1-cos²A

sin²A=1-(2p²/p²+1)²

(a+b)²=a²+b²+2ab

sin²A=1-4p²/p⁴+1+2p²

by taking LCM on R.H.S

sin²A=p⁴+1+2p²-4p²/p⁴+1+2p²

sin²A=p⁴+1-2p²/p⁴+1+2p²

sin²A=(p²-1)²/(p²+1)²

sinA=√(p²-1)²/√(p²+1)²

sinA=(p²-1)/(p²+1)

we know that

cosecA=1/sinA

cosecA=(p²+1)/(p²-1)

Answer,

PLS MARK IT AS BRAINLIEST!!!!

Answer 2

$\huge\mathfrak{Answer :-}$

⭕ Refer to the given attachment !

$\huge\mathfrak{Thank You :)}$