Advertisements
Advertisements
प्रश्न
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
Advertisements
उत्तर
cosec4 A (1 – cos4 A) – 2 cot2 A
= cosec4 A (1 – cos2 A) (1 + cos2 A) – 2 cot2 A
= cosec4 A (sin2 A) (1 + cos2 A) – 2 cot2 A
= cosec2 A (1 + cos2 A) – 2 cot2 A
= `cosec^2A + cos^2A/sin^2A - 2cot^2A `
= cosec2 A + cot2 A – 2 cot2 A
= cosec2 A – cot2 A
= 1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
If `sec theta + tan theta = x," find the value of " sec theta`
If x = a sec θ and y = b tan θ, then b2x2 − a2y2 =
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
