Advertisements
Advertisements
प्रश्न
Prove the following identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
उत्तर
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
L.H.S = sec6 θ
= (sec2 θ)3 = (1 + tan2 θ)3
= 1 + (tan2 θ)3 + 3 (1) (tan2 θ) (1 + tan2 θ) ......[(a + b)3 = a3 + b3 + 3 ab (a + b)]
= 1 + tan6 θ + 3 tan2 θ (1 + tan2 θ)
= 1 + tan6 θ + 3 tan2 θ (sec2 θ)
= 1 + tan6 θ + 3 tan2 θ sec2 θ
= tan6 θ + 3 tan2 θ sec2 θ + 1
L.H.S = R.H.S
APPEARS IN
संबंधित प्रश्न
`"If "\frac{\cos \alpha }{\cos \beta }=m\text{ and }\frac{\cos \alpha }{\sin \beta }=n " show that " (m^2 + n^2 ) cos^2 β = n^2`
Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
Prove the following trigonometric identities.
`(1 + cot A + tan A)(sin A - cos A) = sec A/(cosec^2 A) - (cosec A)/sec^2 A = sin A tan A - cos A cot A`
Prove that:
`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Choose the correct alternative:
`(1 + cot^2"A")/(1 + tan^2"A")` = ?
`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
