Advertisements
Advertisements
प्रश्न
If x = a cos θ and y = b cot θ, show that:
`a^2/x^2 - b^2/y^2 = 1`
Advertisements
उत्तर
`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
संबंधित प्रश्न
Prove the following trigonometric identities.
`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`
Prove that:
`sqrt(sec^2A + cosec^2A) = tanA + cotA`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
If `sec θ = 41/40`, then find values of sin θ, cot θ, cosec θ.
Prove that `sec^2A - "cosec"^2A = (2sin^2A - 1)/(sin^2A *cos^2A)`.
Prove that `sqrt(sec^2 theta + "cosec"^2 theta) = tan theta + cot theta`
sin(45° + θ) – cos(45° – θ) is equal to ______.
