Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq
Advertisements
उत्तर
`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))`
= `sqrt((1 + sinq)/(1 - sinq) . (1+ sinq)/(1 + sinq)) + sqrt((1 - sinq)/(1 + sinq) . (1 - sinq)/(1 - sinq))`
= `sqrt((1 + sinq)^2/(1 - sin^2q)` + `sqrt((1 - sinq)^2/(1 - sin^2q))` = `sqrt((1 + sinq)^2/cos^2q)` + `sqrt((1 - sinq)^2/cos^2q)`
= `(1 + sinq)/cosq + (1 - sinq)/cosq = (1 + sinq + 1 - sinq)/cosq` = `2/cosq`
= 2 secq
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`sin theta/(1 - cos theta) = cosec theta + cot theta`
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
Show that none of the following is an identity:
`sin^2 theta + sin theta =2`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
If `cosec theta = 2x and cot theta = 2/x ," find the value of" 2 ( x^2 - 1/ (x^2))`
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
