Advertisements
Advertisements
Question
Prove that `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
Advertisements
Solution
L.H.S = `sqrt((1 + cos "A")/(1 - cos"A"))`
= `sqrt((1 + cos "A")/(1 - cos "A") xx (1 + cos "A")/(1 + cos "A"))` ......[On rationalising the denominator]
= `sqrt((1 + cos "A")^2/(1 - cos^2 "A"))`
= `sqrt((1 + cos "A")^2/(sin^2 "A")` ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"A" = sin^2"A")]`
= `(1 + cos"A")/"sin A"`
= `1/"sin A" + "cos A"/"sin A"`
= cosec A + cot A
= R.H.S
∴ `sqrt((1 + cos "A")/(1 - cos"A"))` = cosec A + cot A
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following trigonometric identities
tan2 A + cot2 A = sec2 A cosec2 A − 2
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
`((sin A- sin B ))/(( cos A + cos B ))+ (( cos A - cos B ))/(( sinA + sin B ))=0`
If `secθ = 25/7 ` then find tanθ.
If a cos θ − b sin θ = c, then a sin θ + b cos θ =
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
If x = a tan θ and y = b sec θ then
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ
If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`
If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
