Advertisements
Advertisements
Question
Prove the following identities:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`
Advertisements
Solution
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
RELATED QUESTIONS
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
If `sec theta + tan theta = x," find the value of " sec theta`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
Without using trigonometric table , evaluate :
`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`
Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.
tan (90 – θ) = ?
Prove that `(cot A + "cosec" A - 1)/(cot A - "cosec" A + 1) = (1 + cos A)/(sin A)`.
