Advertisements
Advertisements
Question
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Advertisements
Solution
LHS = `(cosecA - sinA)(secA - cosA)`
= `(1/sinA - sinA)(1/cosA - cosA)`
= `((1-sin^2A)/(sinA))((1 - cos^2A)/cosA)`
= `(cos^2A/sinA)(sin^2A/cosA)` = cosA.sinA
RHS = `1/(tanA + cotA)`
= `1/(sinA/cosA + cosA/sinA) = 1/((sin^2A + cos^2A)/(sinA.cosA))` = cosA.sinA
Hence , LHS = RHS
APPEARS IN
RELATED QUESTIONS
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
For ΔABC , prove that :
`sin((A + B)/2) = cos"C/2`
Find A if tan 2A = cot (A-24°).
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
If 3 sin θ = 4 cos θ, then sec θ = ?
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
