Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
उत्तर
We have to prove (sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
We know that `sec^2 theta A - tan^2 theta A = 1`
So, we have
(sec A + tan A - 1)(sec A - tan A + 1) = {sec A + (tan A - 1)}{sec A - (tan A - 1)}
`= sec^2 A - (tan A - 1)^2`
`= sec^2 A - (tan^2 A - 2 tan A + 1)`
`= (sec^2 A - tan^2 A) + 2 tan A - 1`
So we have
(sec A + tan A - 1)(sec A - tan A + 1) = 1 + tan A - 1
= 2 tan A
Hence proved.
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Prove the following trigonometric identities.
`tan A/(1 + tan^2 A)^2 + cot A/((1 + cot^2 A)) = sin A cos A`
Prove that `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2`
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
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
\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to
Prove the following identity :
secA(1 - sinA)(secA + tanA) = 1
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
If sec θ = `25/7`, then find the value of tan θ.
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
Prove the following:
`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Prove the following trigonometry identity:
(sinθ + cosθ)(cosecθ – secθ) = cosecθ.secθ – 2 tanθ
