Question

if sec(a)+tan(a)= p find the value of cosec(a)​

Answer 1

Answer:

Coseca = (p² + 1)/(p²-1)

Step-by-step explanation:

Seca + tana = p

=> 1/cosa + Sina/Cosa = p

=> (1+sina)/cosa = p

Squaring both sides

=> (1+sina)²/Cos²a = p²

=> (1+Sina)²/(1-Sin²a) = p²

=> (1+Sina)²/(1+sina)(1-Sina) = p²

=> (1 +sina)/(1-Sina) = p²

=> 1 + Sina = p² - p²Sina

=> Sina(1+p²) = p²-1

=> Sina = (p²-1)/(p²+1)

Coseca = 1/Sina

=> Coseca = 1/( (p²-1)/(p²+1))

=> Coseca = (p² + 1)/(p²-1)

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 .