Advertisements
Advertisements
प्रश्न
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Prove the following:
(sec2 θ − 1) (cosec2 θ − 1) = 1
Advertisements
उत्तर
We know that
sec2 θ − tan2 θ = 1
cosec2 θ − cot2 θ = 1
So,
(sec2 θ − 1)(cosec2 θ − 1) = tan2 θ × cot2 θ
= (tan θ × cot θ)
= `(tan θ xx 1/tan θ)^2`
= (1)2
= 1
संबंधित प्रश्न
Prove the following trigonometric identities.
`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`
Prove that: `sqrt((sec theta - 1)/(sec theta + 1)) + sqrt((sec theta + 1)/(sec theta - 1)) = 2 cosec theta`
`sin theta (1+ tan theta) + cos theta (1+ cot theta) = ( sectheta+ cosec theta)`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
Prove that:
`"tanθ"/("secθ" – 1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`
If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =
Without using trigonometric table , evaluate :
`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
