Question

If secA + tanA = p then find the value of cosec A . ❤

Answer 1

secA+tanA=p ----------------------------(1)
∵, sec²A-tan²A=1
or, (secA+tanA)(secA-tanA)=1
or, secA-tanA=1/p -----------------------(2)
Subtracting (2) from (1) we get,
2tanA=p-1/p
or, tanA=(p²-1)/2p
∴, cotA=2p/(p²-1)
Now, cosec²A-cot²A=1
or, cosec²A=1+cot²A
or, cosec²A=1+{2p/(p²-1)}²
or, cosec²A=1+4p²/(p²-1)²
or, cosec²A=(p⁴-2p²+1+4p²)/(p²-1)²
or, cosec²A=(p⁴+2p²+1)/(p²-1)²
or, cosec²A=(p²+1)²/(p²-1)²
or, 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 .