Question

If ݏܿ݁ߠ + ݐ݊ܽߠ = ݌ ,then find the value of ܿݏ݋ܿ݁ߠ

Answer 1

when given, secA + tanA = P ......(1)

we know, sec²A - tan²A = 1

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

from equation (1),

P(secA - tanA) = 1

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

adding equations (1) and (2),

2secA = P + 1/P

2secA = (P² + 1)/P

secA = (P² + 1)/2P

cosA = 2P/(P² + 1)

now, sin²A = 1 - cos²A [ from identities ]

sin²A = 1 - [2P/(P² + 1)]²

= 1 - 4P²/(P² + 1)²

= {(P² + 1)² - 4P²}/(P² + 1)²

= {P² + 2P² + 1 - 4P²}/(P² + 1)²

= (P² - 2P² + 1)/(P² + 1)²

= (P² - 1)²/(P² + 1)²

so, sinA = (P² - 1)/(P² + 1)

we know, cosecA = 1/sinA

so, cosecA = (P² + 1)/(P² - 1) [Ans]

Answer 2

hope this answer is helpful