Advertisements
Advertisements
Question
Prove the following identity :
`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`
Advertisements
Solution
LHS = `(1 + sinA)/(1 - sinA)`
RHS = `(cosecA + 1)/(cosecA - 1) = (1/sinA + 1)/(1/sinA - 1)`
= `(1 + sinA)/(1 - sinA)`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(1 + cos A)/sin A = sin A/(1 - cos A)`
The value of sin2 29° + sin2 61° is
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Find the value of `θ(0^circ < θ < 90^circ)` if :
`tan35^circ cot(90^circ - θ) = 1`
If sec θ = `25/7`, then find the value of tan θ.
Prove that sin4A – cos4A = 1 – 2cos2A
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.
