Advertisements
Advertisements
प्रश्न
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Advertisements
उत्तर
LHS = (cosec A - sin A)(sec A - cos A). sec2A
= `(1/sin A - sin A).(1/cos A - cos A). 1/cos^2 A`
= `(1- sin^2A)/sin A.(1- cos^2 A)/(cos A) xx 1/cos^2 A`
= `cos^2 A/sin A xx sin^2 A/cos A xx 1/cos^2 A ....[ ∵ ( 1 - sin^2 A) = cos^2 A, 1 - cos^2 A = sin^2 A]`
= `sin A/cos A = tan A`
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities:
(i) (1 – sin2θ) sec2θ = 1
(ii) cos2θ (1 + tan2θ) = 1
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
`(1 + cos θ + sin θ)/(1 + cos θ - sin θ) = (1 + sin θ)/cos θ`
Prove that:
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
If `( tan theta + sin theta ) = m and ( tan theta - sin theta ) = n " prove that "(m^2-n^2)^2 = 16 mn .`
Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
