Question

if secA+tanA=p then find the value of cosecA

Answer 1

Answer:

cosecA=p²+1/p²-1

Step-by-step explanation:

p²+1/p²-1

Step-by-step explanation:

SecA+tanA=p ----------- (1)

⇒ (secA+tanA)×(secA-tanA)=p×(secA-tanA)

⇒ secA²-tanA²=p×(secA-tanA)

⇒ 1=p×(secA-tanA)

⇒ 1/p= (secA-tanA)

⇒ 1/p= (secA-tanA) ------------- (2)

Now, adding from (1) to (2), we get

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

⇒ 2secA=p²+1/p

⇒ secA=p²+1/2p

Again, subtracting from (1) to (2), we get

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

⇒ 2tanA= p²-1/p

⇒ tanA= p²-1/2p

Hence, secA=p²+1/2p and  tanA= p²-1/2p

We know,

secA/tanA=cosecA=p²+1/2p/p²-1/2p=p²+1/p²-1

So, cosecA=p²+1/p²-1

i hope it will helps you friend

Answer 2

Answer:

Given :

sec A + tan A = p

I am replacing p by ' k '

sec A + tan A = k

We know :

sec A = H / B   & tan A = P / B

H / B + P / B =  k / 1

H + P / B =  k / 1

So , B = 1

H + P = k

P = k - H

From pythagoras theorem :

H² = P² + B²

H² = ( H - k )² + 1

H² = H² + k² - 2 H k + 1

2 H k = k² + 1

H = k² + 1 / 2 k

P = k - H

P = k² - 1 / 2 k

Now write k = p we have :

Base = 1

Perpendicular P = P² - 1 / 2 P

Hypotenuse H = P² + 1 / 2 P

Value of cosec A = H / P

cosec A =  P² + 1 / 2 P / P² - 1 / 2 P

cosec A = P² + 1 / P² - 1

Therefore , we got value .