Advertisements
Advertisements
Question
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
Advertisements
Solution
`a^2/x^2 - b^2/y^2`
= `a^2/(a^2cos^2theta) - b^2/(b^2cot^2theta)`
= `1/cos^2theta - sin^2theta/cos^2theta`
= `(1 - sin^2theta)/cos^2theta`
= `cos^2theta/cos^2theta`
= 1
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(1 - sin θ)/(1 + sin θ) = (sec θ - tan θ)^2`
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Prove the following identities:
`(1 + cos theta - sin^2 theta )/(sin theta (1 + cos theta)) = cot theta`
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove the following identity :
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
If x = r sin θ cos Φ, y = r sin θ sin Φ and z = r cos θ, prove that x2 + y2 + z2 = r2.
If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`
