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 identities:
`sqrt((1 - sinA)/(1 + sinA)) = cosA/(1 + sinA)`
Prove the following identities:
`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`
If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x2 + y2 + z2 = r2
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
Write the value of `3 cot^2 theta - 3 cosec^2 theta.`
If tanθ `= 3/4` then find the value of secθ.
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
If cos A + cos2A = 1, then sin2A + sin4A = ?
