Advertisements
Advertisements
प्रश्न
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Advertisements
उत्तर
L.H.S. = `sinA/(1 + cosA)`
= `sinA/(1 + cosA) xx (1 - cosA)/(1 - cosA)`
= `(sinA(1 - cosA))/(1 - cos^2A)`
= `(sinA(1 - cosA))/sin^2A`
= `(1 - cosA)/sinA`
= `1/sinA - cosA/sinA`
= cosec A – cot A = R.H.S.
संबंधित प्रश्न
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
`sec theta (1- sin theta )( sec theta + tan theta )=1`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
If `tan θ = 13/12`, then cot θ = ?
If tan θ × A = sin θ, then A = ?
Prove that `(sin θ + tan θ)/(cos θ) = tan θ (1 + sec θ)`.
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
