Advertisements
Advertisements
प्रश्न
Prove that `1/("cosec" θ - cot θ) = "cosec" θ + cot θ`.
Advertisements
उत्तर
L.H.S. = `1/("cosec" θ - cot θ)`
= `1/("cosec" θ - cot θ) xx ("cosec" θ + cot θ)/("cosec" θ + cot θ)` ...[On rationalising the denominator]
= `("cosec" θ + cot θ)/("cosec"^2θ - cot^2θ)` ...[∵ (a – b)(a + b) = a2 – b2]
= `("cosec" θ + cot θ)/1` ...`[(∵ 1 + cot^2θ = "cosec"^2θ),(∴ "cosec"^2θ - cot^2θ = 1)]`
= cosec θ + cot θ = R.H.S.
∴ `1/("cosec" θ - cot θ) = "cosec" θ + cot θ`
संबंधित प्रश्न
Prove the following identities:
`(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ`
`(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2`
`(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ`
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Express the ratios cos A, tan A and sec A in terms of sin A.
Prove that `(tan^2 theta)/(sec theta - 1)^2 = (1 + cos theta)/(1 - cos theta)`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove the following identities:
`1 - cos^2A/(1 + sinA) = sinA`
If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
The value of sin ( \[{45}^° + \theta) - \cos ( {45}^°- \theta)\] is equal to
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
Find the value of sin 30° + cos 60°.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)) + sqrt((1 - sin theta)/(1 + sin theta))` = 2 sec θ
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Prove that `(sin θ + "cosec" θ)/(sin θ) = 2 + cot^2θ`.
If cos 9α = sin α and 9α < 90°, then the value of tan 5α is ______.
