Advertisements
Advertisements
प्रश्न
Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.
Advertisements
उत्तर
LHS = cot θ - tan θ
= `cos θ/sin θ - sin θ/cos θ`
= `(cos^2 θ - sin^2 θ)/(sin θ. cos θ)`
= `(cos^2 θ - (1 - cos^2 θ))/(sin θ. cos θ)`
= `(2cos^2 θ - 1)/(sin θ. cos θ)`
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Prove the following identities:
`sinA/(1 + cosA) = cosec A - cot A`
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
`(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 :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.
If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`
