Advertisements
Advertisements
Question
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Advertisements
Solution
`(1 - cosA)/sinA + sinA/(1 - cosA)`
= `((1 - cosA)^2 + sin^2A)/(sinA(1 - cosA))`
= `(1 + cos^2A - 2cosA + sin^2A)/(sinA(1 - cosA))`
= `(2 - 2cosA)/(sinA(1 - cosA))`
= `(2(1 - cosA))/(sinA(1 - cosA))`
= 2 cosec A
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
If x sin3 θ + y cos3 θ = sin θ cos θ and x sin θ = y cos θ, then prove that x2 + y2 = 1
If `1 - cos^2θ = 1/4`, then θ = ?
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
