Advertisements
Advertisements
प्रश्न
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
Advertisements
उत्तर
LHS = `cosA/(1 - tanA) + sinA/(1 - cotA)`
= `cosA/(1-sinA/cosA) + sinA/(1 - cosA/sinA) = cosA/((cosA -sinA)/cosA) + sinA/((sinA - cosA)/sinA)`
= `cos^2A/(cosA - sinA) + sin^2A/(sinA - cosA) = (cos^2A - sin^2A)/((cosA - sinA))`
`((cosA - sinA)(cosA + sinA))/(cosA - sinA)`
= sinA + cosA = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
`sin^2 theta + 1/((1+tan^2 theta))=1`
`1 + (tan^2 θ)/((1 + sec θ)) = sec θ`
` (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 = 2/3 , " write the value of" (4+4 tan^2 theta).`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
