Advertisements
Advertisements
प्रश्न
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
उत्तर
L.H.S. = `sinA/(1 + cosA)`
= `sinA/(1 + cosA) xx (1 - cosA)/(1 - cosA)`
= `(sinA(1 - cosA))/(1 - cos^2A)`
= `(sinA(1 - cosA))/sin^2A`
= `(1 - cosA)/sinA`
= `1/sinA - cosA/sinA`
= cosec A – cot A = R.H.S.
APPEARS IN
संबंधित प्रश्न
Evaluate sin25° cos65° + cos25° sin65°
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
`(cot^2 theta ( sec theta - 1))/((1+ sin theta))+ (sec^2 theta(sin theta-1))/((1+ sec theta))=0`
cos4 A − sin4 A is equal to ______.
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Prove the following identity :
`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`
If sin θ (1 + sin2 θ) = cos2 θ, then prove that cos6 θ – 4 cos4 θ + 8 cos2 θ = 4
