Advertisements
Advertisements
प्रश्न
9 sec2 A − 9 tan2 A is equal to
पर्याय
1
9
8
0
Advertisements
उत्तर
Given:
`9 sec^2 A-9 tan^2 A`
`=9 (sec^2 A-tan^2 A)`
We know that, `sec^2 A-tan^2 A=1`
Therefore, `9 sec^2 A-9 tan^2 A=9`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`
`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`
(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following trigonometric identities
cosec6θ = cot6θ + 3 cot2θ cosec2θ + 1
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
Prove the following identities:
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2A * cos^2B)`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove that:
`cosA/(1 + sinA) = secA - tanA`
` tan^2 theta - 1/( cos^2 theta )=-1`
If tan A = n tan B and sin A = m sin B , prove that `cos^2 A = ((m^2-1))/((n^2 - 1))`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
