Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Advertisements
उत्तर
We need to prove `sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Here, rationaliaing the L.H.S, we get
`sqrt((1 - cos A)/(1 + cos A)) = sqrt((1 - cos A)/(1 +cos A)) xx sqrt((1 - cos A)/(1 - cos A))`
`= sqrt((1 - cos A)^2/(1 - cos^2 A))`
Further using the property, `sin^2 theta + cos^2 theta = 1` we get
So,
`sqrt((1 - cos A)^2/(1 - cos^2 A)) = sqrt((1 - cos A)^2/sin^2 A`
`= (1 - cos A)/sin A`
`= 1/sin A - cos A/sin A`
= cosec A - cot A
Hence proved.
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 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
`1+(tan^2 theta)/((1+ sec theta))= sec theta`
If `(cot theta ) = m and ( sec theta - cos theta) = n " prove that " (m^2 n)(2/3) - (mn^2)(2/3)=1`
Simplify : 2 sin30 + 3 tan45.
If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.
cos4 A − sin4 A is equal to ______.
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity:
`cosA/(1 + sinA) = secA - tanA`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
Prove that `cos θ/sin(90° - θ) + sin θ/cos (90° - θ) = 2`.
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
Show that tan4θ + tan2θ = sec4θ – sec2θ.
