Advertisements
Advertisements
प्रश्न
Prove that `sqrt((1 + cos A)/(1 - cos A)) = "cosec" A + cot A`.
Advertisements
उत्तर
L.H.S. = `sqrt((1 + cos A)/(1 - cos A))`
= `sqrt((1 + cos A)/(1 - cos A) xx (1 + cos A)/(1 + cos A))` ...[On rationalising the denominator]
= `sqrt((1 + cos A)^2/(1 - cos^2 A))`
= `sqrt((1 + cos A)^2/(sin^2 A)` ...`[(∵ sin^2A + cos^2A = 1),(∴ 1 - cos^2A = sin^2A)]`
= `(1 + cos A)/(sin A)`
= `1/(sin A) + (cos A)/(sin A)`
= cosec A + cot A
= R.H.S.
∴ `sqrt((1 + cos A)/(1 - cos A)) = "cosec" A + cot A`
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
From the figure find the value of sinθ.
Prove the following identity :
`(1 - sin^2θ)sec^2θ = 1`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
cos 45° = ?
Prove that 2(sin6A + cos6A) – 3(sin4A + cos4A) + 1 = 0.
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`
