Advertisements
Advertisements
प्रश्न
Prove that `(cos^2θ)/(sinθ) + sin θ = "cosec" θ`.
Advertisements
उत्तर
L.H.S. = `(cos^2θ)/(sinθ) + sin θ`
= `(cos^2θ + sin^2θ)/(sin θ)`
= `1/(sin θ)` ...[∵ sin2θ + cos2θ = 1]
= cosec θ
= R.H.S.
∴ `(cos^2θ)/(sin θ) + sin θ = "cosec" θ`
APPEARS IN
संबंधित प्रश्न
Evaluate
`(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^2 73^@)`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Prove the following trigonometric identities.
if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
(sec θ + tan θ) . (sec θ – tan θ) = ?
Prove that sin6A + cos6A = 1 – 3sin2A . cos2A.
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
