Advertisements
Advertisements
Question
Prove that:
`sqrt((sectheta - 1)/(sec theta + 1)) + sqrt((sectheta + 1)/(sectheta - 1)) = 2cosectheta`
Advertisements
Solution
`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
RELATED QUESTIONS
Without using trigonometric tables evaluate
`(sin 35^@ cos 55^@ + cos 35^@ sin 55^@)/(cosec^2 10^@ - tan^2 80^@)`
Prove the following trigonometric identities.
`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`
Prove the following identities:
`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
Prove the following identities:
`cosA/(1 + sinA) + tanA = secA`
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is ______.
