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
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following trigonometric identities.
`tan theta + 1/tan theta = sec theta cosec theta`
Prove the following trigonometric identities.
`(1 + sec theta)/sec theta = (sin^2 theta)/(1 - cos theta)`
Prove the following trigonometric identities.
`(1 + cos theta + sin theta)/(1 + cos theta - sin theta) = (1 + sin theta)/cos theta`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
`(1+tan^2theta)(1+cot^2 theta)=1/((sin^2 theta- sin^4theta))`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
Write the value of cosec2 (90° − θ) − tan2 θ.
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
Without using trigonometric identity , show that :
`sin(50^circ + θ) - cos(40^circ - θ) = 0`
Prove that:
tan (55° + x) = cot (35° – x)
If x = h + a cos θ, y = k + b sin θ.
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
sin(45° + θ) – cos(45° – θ) is equal to ______.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
If sinθ = `11/61`, then find the value of cosθ using the trigonometric identity.
