Advertisements
Advertisements
प्रश्न
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
Advertisements
उत्तर
(sec θ + tan θ) (1 – sin θ) = cos θ
L.H.S. (sec θ + tan θ) (1 – sin θ)
= `(1/cosθ + sinθ/cosθ)(1 - sinθ)`
= `((1 + sinθ)(1 - sinθ))/cosθ`
= `(1 - sin^2θ)/cosθ`
= `(sin^2θ + cos^2θ - sin^2θ)/cosθ`
= `cos^2θ/cosθ`
= cos θ
= R.H.S.
Hence Proved.
APPEARS IN
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
`(sintheta - 2sin^3theta)/(2costheta - costheta) =tan theta`
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
sin θ × cosec θ = ______
If sec θ + tan θ = x, then sec θ =
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.
Prove the following identities.
`(sin^3"A" + cos^3"A")/(sin"A" + cos"A") + (sin^3"A" - cos^3"A")/(sin"A" - cos"A")` = 2
