Advertisements
Advertisements
प्रश्न
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Advertisements
उत्तर
L.H.S. = `sqrt((1 + sin theta)/(1 - sin theta)`
= `sqrt(((1 + sin theta)(1 + sin theta))/((1 - sin theta)(1 + sin theta))` ...[conjugate (1 − sin θ)]
= `sqrt((1 + sin theta)^2/(1 - sin^2 theta)`
= `sqrt((1 + sin theta)^2/(cos^2 theta)`
= `(1 + sin theta)/(cos theta)`
= `1/cos theta + sin theta/cos theta`
= sec θ + tan θ
L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities:
`(1 - cos^2 A) cosec^2 A = 1`
Prove the following trigonometric identities.
`((1 + tan^2 theta)cot theta)/(cosec^2 theta) = tan theta`
Prove the following identities:
`1/(tan A + cot A) = cos A sin A`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
If x = a tan θ and y = b sec θ then
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3.
