Advertisements
Advertisements
प्रश्न
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
उत्तर
cosec A – cot A
= `1/sinA - cosA/sinA`
= `(1 - cosA)/sinA`
= `(1 - cosA)/sinA xx (1 + cosA)/(1 + cosA)`
= `(1 - cos^2A)/(sinA(1 + cosA)`
= `sin^2A/(sinA(1 + cosA))`
= `sinA/(1 + cosA)`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
Prove the following identity :
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Prove that: sin6θ + cos6θ = 1 - 3sin2θ cos2θ.
Prove that `sec"A"/(tan "A" + cot "A")` = sin A
Prove that sec2θ – cos2θ = tan2θ + sin2θ
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
