Advertisements
Advertisements
प्रश्न
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Advertisements
उत्तर
LHS = cosecθ(1 + cosθ)(cosecθ - cotθ)
= `1/sinθ(1 + cosθ)(1/sinθ - cosθ/sinθ)`
= `((1 + cosθ))/sinθ ((1-cosθ)/sinθ)`
= `(1 - cos^2θ)/sin^2θ = sin^2θ/sin^2θ = 1 = RHS`
APPEARS IN
संबंधित प्रश्न
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
If sin θ + sin2 θ = 1 show that: cos2 θ + cos4 θ = 1
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
