Advertisements
Advertisements
Question
Show that `sqrt((1-cos A)/(1 + cos A)) = sinA/(1 + cosA)`
Advertisements
Solution
`L.H.S = sqrt((1-cosA)/(1 + cosA))`
`= sqrt(((1-cosA)(1 + cosA))/((1+ cosA)(1 + cosA)))`
`= sqrt((1 - cos^2A)/(1 + cosA)^2`
`= sqrt((sin^2A)/(1+cosA)^2)`
`= sinA/(1 + cosA)`
= R.H.S
APPEARS IN
RELATED QUESTIONS
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`sqrt((1+sinA)/(1-sinA)) = secA + tanA`
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`(1 + cos theta - sin^2 theta)/(sin theta (1 + cos theta)) = cot theta`
Prove the following trigonometric identities.
`((1 + sin theta - cos theta)/(1 + sin theta + cos theta))^2 = (1 - cos theta)/(1 + cos theta)`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
For ΔABC , prove that :
`tan ((B + C)/2) = cot "A/2`
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
