Advertisements
Advertisements
प्रश्न
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
उत्तर
LHS = `1/(sin θ + cos θ) + 1/(sin θ - cos θ)`
= `((sin θ - cos θ) + (sin θ + cos θ))/(sin^2 θ - cos^2 θ)`
= `(2 sin θ)/((1 - cos^2 θ) - cos^2 θ)`
= `(2 sin θ)/(1 - 2cos^2 θ)`
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
`sin^6 theta + cos^6 theta =1 -3 sin^2 theta cos^2 theta`
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
If sec θ = `25/7`, then find the value of tan θ.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that `(sintheta + "cosec" theta)/sin theta` = 2 + cot2θ
If 3 sin A + 5 cos A = 5, then show that 5 sin A – 3 cos A = ± 3
Eliminate θ if x = r cosθ and y = r sinθ.
