Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Advertisements
उत्तर
L.H.S. = `(sec A - 1)/(sec A + 1)`
= `(1/(cosA) - 1/1)/(1/(cosA) + 1/1`
= `((1 - cos A)/cos A)/((1 + cos A)/cos A)`
= `(1 - cos A)/cos A xx cos A/(1 + cos A)`
= `(1 - cosA)/(1 + cosA)`
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Write True' or False' and justify your answer the following :
The value of \[\sin \theta\] is \[x + \frac{1}{x}\] where 'x' is a positive real number .
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
Find the value of `θ(0^circ < θ < 90^circ)` if :
`cos 63^circ sec(90^circ - θ) = 1`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that `cot^2 "A" [(sec "A" - 1)/(1 + sin "A")] + sec^2 "A" [(sin"A" - 1)/(1 + sec"A")]` = 0
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
Show that `(cos^2(45^circ + θ) + cos^2(45^circ - θ))/(tan(60^circ + θ) tan(30^circ - θ)) = 1`
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
