Question

if sec teta +tan teta =x find the value of sec teta in term of x only

Answer 1

I have taken P in place of theta because of simplicity in writing

sec p = x – tan p

squaring both the sides

sec² p = x² – 2* x* tan p + tan² p

sec² p – tan² p = x² – 2* x* tan p

x² – 2* x* tan p – 1 = 0

2* x* tan p = x² – 1

tan p = (x² – 1) / 2 x

and here ,

Sec² P - tan² P = 1

( SecP + tanP )( secP - tanP ) = 1

x × ( sec P - tanP ) = 1

Sec P = 1/x + tanP

Sec P = 1/x + (x² -1) 2x

Answer 2

Holaaaa Mate

Answer:

Given that,

secθ - tanθ = x .....(i)

We know that,

sec²θ - tan²θ = 1

=> (secθ + tanθ)(secθ - tanθ) = 1

=> (secθ + tanθ) × x = 1

=> secθ + tanθ = 1/x

So, secθ + tanθ = 1/x [Proved]

secθ + tanθ = 1/x .....(ii)

Now, adding (i) and (ii), we get

2 secθ = x + 1/x

=> secθ = 1/2 (x² + 1)/x

=> cosθ = 2x/(x² + 1)

So, cosθ = 2x/(x² + 1)

Now,

sinθ = [√{(x² + 1)² - (2x)²}]/(x² + 1)

= (x² - 1)/(x² + 1)

hope it helps..!!!❤