Advertisements
Advertisements
प्रश्न
Write the value of `(1 + tan^2 theta ) cos^2 theta`.
उत्तर
`(1+ tan^2 theta ) cos^2 theta `
= `sec^2 theta xx 1/ sec^2 theta`
=1
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities
sec4 A(1 − sin4 A) − 2 tan2 A = 1
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove that:
(cosec A – sin A) (sec A – cos A) sec2 A = tan A
`sin^2 theta + cos^4 theta = cos^2 theta + sin^4 theta`
`(sec theta + tan theta )/( sec theta - tan theta ) = ( sec theta + tan theta )^2 = 1+2 tan^2 theta + 25 sec theta tan theta `
If` (sec theta + tan theta)= m and ( sec theta - tan theta ) = n ,` show that mn =1
If sinθ = `11/61`, find the values of cosθ using trigonometric identity.
Prove the following identity :
(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`
Prove the following identity :
`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that `(sin (90° - θ))/cos θ + (tan (90° - θ))/cot θ + (cosec (90° - θ))/sec θ = 3`.
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
Prove that cot2θ – tan2θ = cosec2θ – sec2θ
The value of the expression [cosec(75° + θ) – sec(15° – θ) – tan(55° + θ) + cot(35° – θ)] is ______.
Given that sin θ = `a/b`, then cos θ is equal to ______.
Complete the following activity to prove:
cotθ + tanθ = cosecθ × secθ
Activity: L.H.S. = cotθ + tanθ
= `cosθ/sinθ + square/cosθ`
= `(square + sin^2theta)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ....... ∵ `square`
= `1/sinθ xx 1/cosθ`
= `square xx secθ`
∴ L.H.S. = R.H.S.
If tan θ = `x/y`, then cos θ is equal to ______.
