Advertisements
Advertisements
प्रश्न
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Advertisements
उत्तर
LHS = `( tan A + sec A - 1)/(tan A - sec A + 1)`
= `(( tan A + sec A) - (sec^2 A - tan^2 A))/((tan A - sec A) + 1)`
= `(( tan A + sec A)( 1 - sec A + tan A))/(tan A - sec A + 1)`
= tan A + sec A
= `sin A/cos A + 1/cos A = (1 + sin A)/cos A`
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
Prove the following trigonometric identities.
tan2 A sec2 B − sec2 A tan2 B = tan2 A − tan2 B
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove that:
`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`
`(sec^2 theta -1)(cosec^2 theta - 1)=1`
`(sin theta +cos theta )/(sin theta - cos theta)+(sin theta- cos theta)/(sin theta + cos theta) = 2/((sin^2 theta - cos ^2 theta)) = 2/((2 sin^2 theta -1))`
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
