Advertisements
Advertisements
Question
Prove the following identities:
`sinA/(1 - cosA) - cotA = cosecA`
Advertisements
Solution
`sinA/(1 - cosA) - cotA`
= `sinA/(1 - cosA) - cosA/sinA`
= `(sin^2A - cosA + cos^2A)/((1 - cosA)sinA)`
= `(1 - cosA)/((1 - cosA)sinA)`
= `1/sinA`
= cosec A
RELATED QUESTIONS
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`cot^2 theta - 1/(sin^2 theta ) = -1`a
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.
