Advertisements
Advertisements
प्रश्न
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
Advertisements
उत्तर
L.H.S. = cosec A(1 + cos A) (cosecA – cot A)
= `1/(sin A)(1 + cos A)(1/(sin A) - (cos A)/(sin A))`
`((1-cos A)/sin A)`
`1/sin A(1+cos A)((1-cos A)/sin A)`
`= ((1+ cos A)(1-cos A))/sin^2 A`
Apply the identity (1 + cosA) (1 − cosA) = 1 − cos2A
`= (1-cos^2A)/sin^2A`
`= sin^2A/sin^2A = 1`
cscA(1 + cosA) (cscA − cotA) = 1 proved
संबंधित प्रश्न
Prove the following trigonometric identities:
sin2 A cot2 A + cos2 A tan2 A = 1
Given that: (1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
(1 + cot A – cosec A)(1 + tan A + sec A) = 2
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos ^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
If tan α + cot α = 2, then tan20α + cot20α = ______.
