Advertisements
Advertisements
प्रश्न
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
Advertisements
उत्तर
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
L.H.S = `(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")`
= `((sin"A" + cos"A")(sin^2"A" - sin"A"cos"A" + cos^2"A"))/((sin"A" + cos"A")) + ((sin"A" - cos"A")(sin^2"A" + sin"A"cos"A" + cos^2"A"))/((sin"A" - cos"A"))`
= (sin2 A + cos2 A) − sin A cos A + (sin2 A + cos2 A) + sin A cos A
= 1 + 1
= 2
L.H.S = R.H.S
∴`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
If cos θ + cos2 θ = 1, prove that sin12 θ + 3 sin10 θ + 3 sin8 θ + sin6 θ + 2 sin4 θ + 2 sin2 θ − 2 = 1
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
Show that none of the following is an identity:
`sin^2 theta + sin theta = 2`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`
Prove that sin2 θ + cos4 θ = cos2 θ + sin4 θ.
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
