Advertisements
Advertisements
Question
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
Advertisements
Solution
L.H.S. = `(1 + sec A)/(sec A)`
= `1/(sec A) + (sec A)/(sec A)`
= cos A + 1
= `(1 + cos A) xx (1 - cos A)/(1 - cos A)`
= `(1 - cos^2A)/(1 - cosA)`
= `(sin^2A)/(1 - cosA)` ...`[(∵ sin^2A + cos^2A = 1),(∴ 1 - cos^2A = sin^2A)]`
= R.H.S.
∴ `(1 + sec A)/(sec A) = (sin^2A)/(1 - cosA)`
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
Prove the following trigonometric identities
`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that (x2 – y2) = (a2 – b2).
Write the value of `(cot^2 theta - 1/(sin^2 theta))`.
If ` cot A= 4/3 and (A+ B) = 90° ` ,what is the value of tan B?
If `sqrt(3) sin theta = cos theta and theta ` is an acute angle, find the value of θ .
Define an identity.
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Prove the following identities.
`(sin "A" - sin "B")/(cos "A" + cos "B") + (cos "A" - cos "B")/(sin "A" + sin "B")`
If x = a tan θ and y = b sec θ then
If `cos θ = 24/25`, then sin θ = ?
(1 – cos2 A) is equal to ______.
