Advertisements
Advertisements
प्रश्न
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
Advertisements
उत्तर १
L.H.S = (sin θ + cosec θ)2 + (cos θ + sec θ)2
= (sin2θ + cosec2θ + 2 sin θ cosec θ + cos2θ + sec2θ + 2cos θ sec θ)
= (sin2θ + cos2θ) + (cosec2θ + sec2θ) + 2 sin θ `(1/("sin"theta)) + 2 cos theta (1/("cos" theta))`
= (1) + (1 + cot2θ + 1 + tan2θ) + (2) + (2)
= 7 + tan2θ + cot2θ
= R.H.S
उत्तर २
L.H.S = (sin θ + cosec θ)2 + (cos θ + sec θ)2
= (sin2θ + cosec2θ + 2 sin θ cosec θ + cos2θ + sec2θ + 2cos θ sec θ)
= (sin2θ + cos2θ ) + 1 + cot2θ + 2 sin θ x `1/sin θ` + 1 + tan2 θ + 2cos θ. `1/cos θ`
= 1 + 1 + 1 + 2 + 2 + tan2 θ + cot2θ
= 7 + tan2 θ + cot2θ
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`1/(1 + sin A) + 1/(1 - sin A) = 2sec^2 A`
Prove the following trigonometric identities. `(1 - cos A)/(1 + cos A) = (cot A - cosec A)^2`
Prove the following trigonometric identities.
`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
Find the value of `(cos 38° cosec 52°)/(tan 18° tan 35° tan 60° tan 72° tan 55°)`
Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
cot θ . tan θ = ?
(sec θ + tan θ) . (sec θ – tan θ) = ?
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
