Advertisements
Advertisements
प्रश्न
Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`
उत्तर
L.H.S = `(sin theta)/(1 - cot theta) + (cos theta)/(1- tan theta)`
`= (sin theta)/(1 - cos theta/sin theta) + cos theta/(1 - sin theta/cos theta)`
`= sin^2 theta/(sin theta - cos theta) + cos^2 theta/(cos theta - sin theta)`
`= (sin^2 theta)/(sin theta - cos theta) - cos^2 theta/(sin theta - costheta)`
`= (sin^2 theta - cos^2 theta)/(sin theta - cos theta)`
`= ((sin theta - cos theta)(sin theta + cos theta))/(sin theta - cos theta)`
`= sin theta + cos theta`
= R.H.S
APPEARS IN
संबंधित प्रश्न
`Prove the following trigonometric identities.
`(sec A - tan A)^2 = (1 - sin A)/(1 + sin A)`
Prove the following identities:
(sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
`sin theta/((cot theta + cosec theta)) - sin theta /( (cot theta - cosec theta)) =2`
Prove the following identity :
`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
Prove that `sqrt((1 - sin θ)/(1 + sin θ)) = sec θ - tan θ`.
If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`
If cos θ = `24/25`, then sin θ = ?
If cosA + cos2A = 1, then sin2A + sin4A = 1.
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
