Advertisements
Advertisements
प्रश्न
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
Advertisements
उत्तर
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
L.H.S = [(sin θ + sec θ)2 + (cos θ + cosec θ)2]
= [sin2 θ + sec2 θ + 2 sin θ sec θ + cos2 θ + cosec2 θ + 2 cos θ cosec θ]
= (sin2θ + cos2θ) + (sec2θ + cosec2θ) + 2 (sinθ secθ + cos θ cosec θ)
= `1 + sec^2 theta + "cosec"^2 theta + 2[sin theta xx 1/cos theta + cos theta xx 1/sin theta]`
= `1 + sec^2 theta + "cosec"^2 theta + 2 [(sin^2 theta + cos^2 theta)/(sintheta cos theta)]`
= `1 + sec^2 theta + "cosec"^2 theta + 2 xx 1/(sintheta costheta)`
= 1 + sec2θ + cosec2θ + 2 secθ cosecθ
= 1 + (secθ + cosecθ)2
L.H.S = R.H.S
∴ (sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
APPEARS IN
संबंधित प्रश्न
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
Find the value of sin ` 48° sec 42° + cos 48° cosec 42°`
Prove the following identity :
( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
If `cos theta/(1 + sin theta) = 1/"a"`, then prove that `("a"^2 - 1)/("a"^2 + 1)` = sin θ
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
