Advertisements
Advertisements
प्रश्न
Prove that sin4A – cos4A = 1 – 2cos2A
Advertisements
उत्तर
L.H.S = sin4A – cos4A
= (sin2A)2 – (cos2A)2
= (sin2A + cos2A)(sin2A – cos2A) .....[∵ a2 – b2 = (a + b)(a – b)]
= (1)(sin2A – cos2A) ......[∵ sin2A + cos2A = 1]
= sin2A – cos2A
= (1 – cos2A) – cos2A ......`[(because sin^2"A" + cos^2"A" = 1),(therefore 1 - cos^2"" = sin^2"A")]`
= 1 – 2cos2A
= R.H.S
∴ sin4A – cos4A = 1 – 2cos2A
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`
Prove the following trigonometric identities.
`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
If `sec theta + tan theta = x," find the value of " sec theta`
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
Prove the following identity :
`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`
Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
Choose the correct alternative:
sec2θ – tan2θ =?
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
Prove that
sin2A . tan A + cos2A . cot A + 2 sin A . cos A = tan A + cot A
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
If tan θ = `x/y`, then cos θ is equal to ______.
