Advertisements
Advertisements
प्रश्न
Prove the following identities:
`(secA - tanA)/(secA + tanA) = 1 - 2secAtanA + 2tan^2A`
Advertisements
उत्तर
L.H.S. = `(secA - tanA)/(secA + tanA)`
= `(secA - tanA)/(secA + tanA) xx (secA - tanA)/(secA - tanA)`
= `(secA - tanA)^2/(sec^2A - tan^2A)`
= `(sec^2A + tan^2A - 2secAtanA)/1`
= 1 + tan2 A + tan2 A – 2 sec A tan A
= 1 – 2 sec A tan A + 2 tan2 A = R.H.S.
संबंधित प्रश्न
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
`cot^2 theta - 1/(sin^2 theta ) = -1`a
`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta`
`(1+ tan^2 theta)/(1+ tan^2 theta)= (cos^2 theta - sin^2 theta)`
Prove the following identity :
`(cotA + tanB)/(cotB + tanA) = cotAtanB`
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
If (sin α + cosec α)2 + (cos α + sec α)2 = k + tan2α + cot2α, then the value of k is equal to
Prove that `(1 + sin θ)/(1 - sin θ) = (sec θ + tan θ)^2`.
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
