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
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`
Write the value of tan10° tan 20° tan 70° tan 80° .
If cosec2 θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.
sec4 A − sec2 A is equal to
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
