Advertisements
Advertisements
प्रश्न
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
Advertisements
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
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`(1+ cos theta - sin^2 theta )/(sin theta (1+ cos theta))= cot theta`
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Write the value of `sin theta cos ( 90° - theta )+ cos theta sin ( 90° - theta )`.
Prove the following identity :
secA(1 - sinA)(secA + tanA) = 1
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
Prove that sin4θ - cos4θ = sin2θ - cos2θ
= 2sin2θ - 1
= 1 - 2 cos2θ
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove the following identities.
cot θ + tan θ = sec θ cosec θ
sec 60° = ?
cot θ . tan θ = ?
If `tan θ = 13/12`, then cot θ = ?
`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`
sec θ when expressed in term of cot θ, is equal to ______.
