Advertisements
Advertisements
प्रश्न
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
Advertisements
उत्तर १
L.H.S. = `1/(secA + tanA)`
= `1/(1/cosA + sinA/cosA)`
= `1/((1 + sinA)/cosA)`
= `cosA/(1 + sinA) xx (1 - sinA)/(1 + sinA)`
= `(cosA(1 - sinA))/((1)^2 - sin^2A)`
= `(cosA(1 - sinA))/cos^2A`
= `1/cosA - sinA/cosA`
= sec A – tan A
L.H.S. = R.H.S.
Hence proved.
उत्तर २
L.H.S = `1/(secA + tanA)`
= `((secA - tanA))/((secA + tanA)(secA - tanA))` ...((Multiply Num. and Deno. by sec A – tan A)
= `(secA - tanA)/(sec^2A - tan^2A)`
= `(secA - tanA)/1` ...[∵ sec2 A – tan2 A = 1]
= sec A – tan A
= R.H.S.
संबंधित प्रश्न
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`
Write the value of tan1° tan 2° ........ tan 89° .
From the figure find the value of sinθ.
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Find the value of sin 30° + cos 60°.
Prove that `((tan 20°)/(cosec 70°))^2 + ((cot 20°)/(sec 70°))^2 = 1`
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
If sec θ + tan θ = `sqrt(3)`, complete the activity to find the value of sec θ – tan θ
Activity:
`square` = 1 + tan2θ ......[Fundamental trigonometric identity]
`square` – tan2θ = 1
(sec θ + tan θ) . (sec θ – tan θ) = `square`
`sqrt(3)*(sectheta - tan theta)` = 1
(sec θ – tan θ) = `square`
