Advertisements
Advertisements
प्रश्न
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
Advertisements
उत्तर
sin3θ + cos3θ
= (sin θ + cos θ)(sin2θ + cos2 – sin θ cos θ)
= (sin θ + cos θ)(1 – sin θ cos θ). ...(i)
L.H.S = `(sin^3θ + cos^3θ)/(sinθ + cosθ) + sinθcosθ`
= `((sinθ + cosθ)(1 - sinθcosθ))/((sinθ + cosθ)) + sinθcosθ` ...(From(i))
= 1 – sin θ cos θ + sin θ.cos θ
Simplify by cancelling – sin θ cos θ and + sin θ.cos θ
= 1
= R.H.S.
संबंधित प्रश्न
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove the following trigonometric identities.
`1 + cot^2 theta/(1 + cosec theta) = cosec theta`
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
Prove the following identity :
tanA+cotA=secAcosecA
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
