Advertisements
Advertisements
प्रश्न
Prove that:
(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1
Advertisements
उत्तर
(tan A + cot A) (cosec A – sin A) (sec A – cos A)
= `(sinA/cosA + cosA/sinA)(1/sinA - sinA)(1/cosA - cosA)`
= `((sin^2A + cos^2A)/(sinAcosA))((1 - sin^2A)/sinA)((1 - cos^2A)/cosA)`
= `(1/(sinAcosA))(cos^2A/sinA)(sin^2A/cosA)`
= 1
संबंधित प्रश्न
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
If cosθ + sinθ = `sqrt2` cosθ, show that cosθ - sinθ = `sqrt2` sinθ.
Prove that
`(cot "A" + "cosec A" - 1)/(cot"A" - "cosec A" + 1) = (1 + cos "A")/"sin A"`
The value of tan A + sin A = M and tan A - sin A = N.
The value of `("M"^2 - "N"^2) /("MN")^0.5`
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
