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 trigonometric identities.
`(cosec A)/(cosec A - 1) + (cosec A)/(cosec A = 1) = 2 sec^2 A`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Prove that:
`(sin^2θ)/(cosθ) + cosθ = secθ`
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove the following identity :
secA(1 + sinA)(secA - tanA) = 1
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Choose the correct alternative:
cos θ. sec θ = ?
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
