if sec teta +tan teta =x find the value of sec teta in term of x only
Answers
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
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..!!!❤