Advertisements
Advertisements
Question
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
Solution
R.H.S. = `(1 - sinA)/(1 + sinA)`
= `(1 - 1/(cosecA))/(1 + 1/(cosecA))`
= `(cosecA - 1)/(cosecA + 1)`
= `(cosecA - 1)/(cosecA + 1) xx (cosecA + 1)/(cosecA + 1)`
= `(cosec^2A - 1)/(cosecA + 1)^2 = cot^2A/(cosecA + 1)^2` ...(∵ cosec2 A – 1 = cot2 A)
= L.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
If tan θ = `7/24`, then to find value of cos θ complete the activity given below.
Activity:
sec2θ = 1 + `square` ......[Fundamental tri. identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square/576`
sec2θ = `square/576`
sec θ = `square`
cos θ = `square` .......`[cos theta = 1/sectheta]`
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
Prove the following:
(sin α + cos α)(tan α + cot α) = sec α + cosec α
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
