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:
cosec4 A – cosec2 A = cot4 A + cot2 A
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
If `sin theta = x , " write the value of cot "theta .`
Write the value of cosec2 (90° − θ) − tan2 θ.
Prove the following identity :
`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to
If 3 sin θ = 4 cos θ, then sec θ = ?
