Advertisements
Advertisements
प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
Advertisements
उत्तर
L.H.S
= `(cosec θ – cot θ)^2`
= `(1/sintheta - costheta/sintheta)^2`
= `(1-costheta)^2/(sin^2 theta)`
= `(1-cos theta)^2/(1-cos^2theta)`
= `((1-costheta)(1-costheta))/((1-costheta)(1+cos theta)) `
= `(1-cos theta)/(1+costheta)`
= R.H.S
संबंधित प्रश्न
Prove the following trigonometric identities:
`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, show that `x^2/a^2 + y^2/b^2 - x^2/c^2 = 1`
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Find A if tan 2A = cot (A-24°).
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = "cosec" θ - cot θ`.
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Prove that cot2θ × sec2θ = cot2θ + 1
Prove that `sintheta/(sectheta+ 1) +sintheta/(sectheta - 1)` = 2 cot θ
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
