Advertisements
Advertisements
प्रश्न
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Advertisements
उत्तर
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = sqrt(sectheta - 1)/sqrt(sectheta + 1) + sqrt(sectheta + 1)/sqrt(sectheta - 1)`
= `(sqrt(sectheta - 1)sqrt(sectheta - 1) + sqrt(sectheta + 1)sqrt(sectheta + 1))/(sqrt(sectheta + 1)sqrt(sectheta - 1))`
= `((sqrt(sectheta - 1))^2 + (sqrt(sectheta + 1))^2)/sqrt((sectheta - 1)(sectheta + 1))`
= `(sectheta - 1 + sectheta + 1)/sqrt(sec^2theta - 1)`
= `(2sectheta)/sqrt(tan^2theta)`
= `(2sectheta)/tantheta`
= `(2 1/costheta)/(sintheta/costheta)`
= `2 1/sintheta`
= `2 cosectheta`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
cosec4 θ − cosec2 θ = cot4 θ + cot2 θ
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
(1 + sin A)(1 – sin A) is equal to ______.
