Advertisements
Advertisements
Question
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
Options
\[\frac{x^2 + 1}{x}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x^2 + 1}{2x}\]
\[\frac{x^2 - 1}{2x}\]
Solution
Given:
`sec θ+tanθ=x`
We know that,
`sec^2 θ-tan^2 θ=1`
⇒` (sec θ+tan θ)(sec θ-tanθ)=1`
⇒`x(sec θ-tan θ)=1`
⇒ `secθ-tan θ=1/x`
Now,
`secθ+tan θ=x,`
`sec θ-tan θ=1/x`
Subtracting the second equation from the first equation, we get
`(secθ+tan θ)-(secθ-tanθ)=x-1/x`
⇒` secθ+tanθ-secθ+tanθ=(x^2-1)/x`
⇒ `2 tanθ=(x^2-1)/x`
⇒ `2 tan θ=(x^2-1)/(2x)`
⇒ `tan θ=(x^2-1)/(2x)`
APPEARS IN
RELATED QUESTIONS
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove that `sqrt((1 + cos theta)/(1 - cos theta)) + sqrt((1 - cos theta)/(1 + cos theta)) = 2 cosec theta`
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
If `sec theta + tan theta = p,` prove that
(i)`sec theta = 1/2 ( p+1/p) (ii) tan theta = 1/2 ( p- 1/p) (iii) sin theta = (p^2 -1)/(p^2+1)`
Define an identity.
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
Prove that `(cos(90 - "A"))/(sin "A") = (sin(90 - "A"))/(cos "A")`
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
Prove that `(1 + sin "B")/"cos B" + "cos B"/(1 + sin "B")` = 2 sec B
If tan α + cot α = 2, then tan20α + cot20α = ______.
Show that tan4θ + tan2θ = sec4θ – sec2θ.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
