Advertisements
Advertisements
प्रश्न
Prove the following identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Advertisements
उत्तर
L.H.S. = `sqrt((1 - sinA)/(1 + sinA))`
= `sqrt((1 - sinA)/(1 + sinA) xx (1 + sinA)/(1 + sinA))`
= `sqrt((1 - sin^2A)/(1 + sinA)^2)`
= `sqrt(cos^2A/(1 + sinA)^2)`
= `cosA/(1 + sinA)` = R.H.S.
संबंधित प्रश्न
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
sin(45° + θ) – cos(45° – θ) is equal to ______.
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
