Advertisements
Advertisements
प्रश्न
If tan θ + cot θ = 2, then tan2θ + cot2θ = ?
Advertisements
उत्तर
tan θ + cot θ = 2 ....[Given]
∴ (tan θ + cot θ)2 = 4 .....[Squaring both sides]
∴ tan2θ + 2tan θ.cot θ + cot2θ = 4 ......[∵ (a + b)2 = a2 + 2ab + b2]
∴ tan2θ + 2(1) + cot2θ = 4 ......[∵ tan θ ⋅ cot θ = 1]
∴ tan2θ + cot2θ = 4 – 2
∴ tan2θ + cot2θ = 2
APPEARS IN
संबंधित प्रश्न
Prove the following identities:
`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`
`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`
`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec2 A = 1 cot2 A.
Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
Prove the following trigonometric identities.
`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
`cos A/(1 - tan A) + sin A/(1 - cot A) = sin A + cos A`
Prove the following trigonometric identities.
(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove that:
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
If `( cos theta + sin theta) = sqrt(2) sin theta , " prove that " ( sin theta - cos theta ) = sqrt(2) cos theta`
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Write the value of sin A cos (90° − A) + cos A sin (90° − A).
Prove the following identity:
tan2A − sin2A = tan2A · sin2A
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Prove the following identity :
`(cosecθ)/(tanθ + cotθ) = cosθ`
Find the value of sin 30° + cos 60°.
If sec θ = x + `1/(4"x"), x ≠ 0,` find (sec θ + tan θ)
