Advertisements
Advertisements
प्रश्न
Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.
Advertisements
उत्तर
L.H.S. = (sin θ + cos θ)(tan θ + cot θ)
= `(sin theta + cos theta)(sin theta/cos theta + costheta/sin theta)`
= `(sin theta + cos theta)((sin^2 theta + cos^2 theta)/(costhetasin theta))`
= `(sintheta+costheta)xx1/(sinthetacostheta)` ...[∵ sin2θ + cos2θ = 1]
= `(sin theta + cos theta)/(cos theta sin theta)`
= `sin theta/(cos thetasin theta) + cos theta/(cos theta sin theta)`
= `1/cos theta + 1/sin theta`
= `sec theta + cosec theta`
= R.H.S
Hence proved.
APPEARS IN
संबंधित प्रश्न
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
if `cosec theta - sin theta = a^3`, `sec theta - cos theta = b^3` prove that `a^2 b^2 (a^2 + b^2) = 1`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
If tan θ = `x/y`, then cos θ is equal to ______.
