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.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities.
`(1 + tan^2 A) + (1 + 1/tan^2 A) = 1/(sin^2 A - sin^4 A)`
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
If sin θ + cos θ = x, prove that `sin^6 theta + cos^6 theta = (4- 3(x^2 - 1)^2)/4`
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
