Advertisements
Advertisements
प्रश्न
Prove that:
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1
Advertisements
उत्तर
Taking LHS
(cosec θ - sinθ )(secθ - cos θ ) ( tanθ +cot θ)
`(1/(sin theta )- sin theta )(1/(cos θ )- cosθ )((sin θ)/(cos θ) +(cos θ)/(sin θ))`
`=((1-sin^2 θ)/(sin θ)) ((1- cos ^2θ)/(cos θ)) ((sin^2 θ + cos^2 θ)/(sin θ . cos θ))`
`= (cos^2 θ)/( sin θ) xx (sin^2 θ)/(cos θ ) xx 1/(sinθ . cos θ )` = 1 = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`
If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`
If `sec theta + tan theta = x," find the value of " sec theta`
Prove that:
Sin4θ - cos4θ = 1 - 2cos2θ
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
If sec θ = `25/7`, find the value of tan θ.
Solution:
1 + tan2 θ = sec2 θ
∴ 1 + tan2 θ = `(25/7)^square`
∴ tan2 θ = `625/49 - square`
= `(625 - 49)/49`
= `square/49`
∴ tan θ = `square/7` ........(by taking square roots)
cot θ . tan θ = ?
Prove the following:
`1 + (cot^2 alpha)/(1 + "cosec" alpha)` = cosec α
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
