Advertisements
Advertisements
प्रश्न
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
Advertisements
उत्तर
LHS = `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ))`
LHS = `(sin^2 θ/cos θ). (cos^2 θ/sin θ)`
LHS = sin θ. cos θ
RHS = `1/(tan θ + cot θ)`
RHS = `1/((sin^2 θ + cos^2 θ)/(sin θ. cos θ))`
RHS = `(sin θ. cos θ)/(sin^2 θ + cos^2 θ)`
RHS = sin θ. cos θ
LHS = RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(1+ secA)/sec A = (sin^2A)/(1-cosA)`
[Hint : Simplify LHS and RHS separately.]
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Prove the following trigonometric identities:
tan2 A + cot2 A = sec2 A cosec2 A − 2
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`
`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec theta)`
Prove the following identities:
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta )/(cos theta)`
If `(x/a sin theta - y/b cos theta) = 1` and `(x/a cos theta + y/b sin theta) = 1`, prove that `(x^2/a^2 + y^2/b^2) = 2`.
If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a2 + b2 =
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
If `sin θ + cos θ = sqrt(3)`, then show that tan θ + cot θ = 1.
