Advertisements
Advertisements
Question
If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.
Advertisements
Solution
Let `x/a=y/b = z/c` = k
=> x = ak, y = bk, z = ck
L.H.S = `x^3/a^3 + y^3/b^3 + z^3/c^3`
`= (ak)^3/(a^3) + (bk)^3/b^3 + (ck)^3/c^3`
`= (a^3k^3)/a^3 + (b^3k^3)/b^3 + (c^3k^3)/c^3`
`= k^3 + k^3 + k^3`
= `3k^3`
R.H.S = `(3xyz)/(abc)`
`= (3(ak)(bk)(ck))/(abc)`
`= (3(k^3)(abc))/(abc)`
`= 3k^3`
= L.H.S
=> L.H.S = R.H.S
`=> x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`
APPEARS IN
RELATED QUESTIONS
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
`sin^2 A + 1/(1 + tan^2 A) = 1`
Prove the following trigonometric identities.
`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Prove the following identity :
`1/(tanA + cotA) = sinAcosA`
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
If tan θ – sin2θ = cos2θ, then show that `sin^2θ = 1/2`.
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
