Advertisements
Advertisements
प्रश्न
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
उत्तर
Given:
`cosecθ=2x, cot θ2/x`
We know that,
`cosec^2 θ-cot^2 θ=1`
⇒` (2x)^2-(2/x)^2=1`
⇒` 4x^2-4/x^2=1`
⇒ `4(x^2-1/x^2)=1`
⇒`2xx2xx(x^2-1/x^2)=1`
⇒ `2(x^2-1/x^2)=1/2`
APPEARS IN
संबंधित प्रश्न
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
`sin^2 theta + 1/((1+tan^2 theta))=1`
Prove the following identity :
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or `1/2`.
sin(45° + θ) – cos(45° – θ) is equal to ______.
