Advertisements
Advertisements
प्रश्न
Prove the following identity :
`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`
Advertisements
उत्तर
`tanA - cotA = sinA/cosA - cosA/sinA`
= `(sin^2A - cos^2A)/(sinAcosA)`
= `(1 - cos^2A - cos^2A)/(sinAcosA)` (`Q sin^2A = 1 - cos^2A`)
= `(1 - 2cos^2A)/(sinAcosA)`
APPEARS IN
संबंधित प्रश्न
If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
