Advertisements
Advertisements
प्रश्न
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Advertisements
उत्तर
LHS:
`sqrt(sec^2theta + cosec^2theta)`
`= sqrt(1/cos^2theta + 1/sin^2theta)`
Taking LCM:
`= sqrt ((sin^2theta + cos^2theta)/(sin^2 theta cos^2theta))`
Using the identity sin2θ + cos2θ = 1:
`= sqrt(1/(sin^2theta cos^2theta))`
`= 1/(sintheta costheta)`
RHS:
tanθ + cotθ
`= sintheta/costheta + costheta/sintheta`
Taking LCM:
`= (sin^2theta + cos^2theta)/(sintheta costheta)`
Using sin2θ + cos2θ = 1:
`= 1/(sintheta costheta)`
LHS = RHS
`sqrt(sec^2theta + cosec^2theta) = tantheta + cottheta`
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
Show that : tan 10° tan 15° tan 75° tan 80° = 1
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
If a cot θ + b cosec θ = p and b cot θ − a cosec θ = q, then p2 − q2
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`
Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
