Advertisements
Advertisements
Question
Prove the following identities:
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
Solution
`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`
= L.H.S.
= `(sec"A"-1)/(sec"A"+1)`
= `(1/cosA-1)/(1/cosA+1)`
=`(1-cosA)/(1+cosA)`
Multiplied by 1 + cosA
=`(1-cos^2A)/(1+cosA)^2`
=`(sin^2A)/(1+cosA)^2`
=`((sinA)/(1+cosA))^2`
= R.H.S
Hence Proved.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following trigonometric identities
If x = a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 − y2 = a2 − b2
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
Prove the following identities:
`cosecA - cotA = sinA/(1 + cosA)`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Prove that sin (90° - θ) cos (90° - θ) = tan θ. cos2θ.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
