Question

If secA-tanA=p then find the value of tanA

Answer 1

Answer:

sec A- tan A=p

1/cos A - sin A/cos A=p

(1-sin A)/cosA=p

sin A=(1-p^2)/(1+p^2)

cos A=2p/(1+p^2)

tan A=sin A/cos A

tan A=(1-p^2)/2p

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 tan A = P / B

tan A =  P² - 1 / 2 P / 1

tan A =  P² - 1 / 2 P

Therefore , we got value .