Advertisements
Advertisements
Questions
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`.
Prove the following:
`sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`
Advertisements
Solution
LHS = `sqrt((1 - cos θ)/(1 + cos θ) xx (1 - cos θ)/(1 - cos θ))`
= `sqrt((1 - cos θ)^2/(1 - cos^2θ))`
= `(1 - cos θ)/(sqrt(1 - cos^2θ))`
= `(1 - cos θ)/(sqrt(sin^2θ))`
= `(1 - cos θ)/(sin θ)`
= `(1)/(sin θ) - (cos θ)/(sin θ)`
= cosec θ − cot θ
= RHS
Hence proved.
RELATED QUESTIONS
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Prove that:
`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.
If cosec θ − cot θ = α, write the value of cosec θ + cot θ.
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.
Prove that sin6A + cos6A = 1 – 3sin2A . cos2A.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
