Advertisements
Advertisements
प्रश्न
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ.
Advertisements
उत्तर
L.H.S. = sec2θ + cosec2θ
= `1/(cos^2θ) + 1/(sin^2θ)`
= `(sin^2θ + cos^2θ)/(cos^2θ.sin^2θ)`
= `1/(cos^2θ.sin^2θ)` ...[∵ sin2θ + cos2θ = 1]
= `1/(cos^2θ) xx 1/(sin^2θ)`
= sec2θ × cosec2θ
= R.H.S.
∴ sec2θ + cosec2θ = sec2θ × cosec2θ
APPEARS IN
संबंधित प्रश्न
If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.
Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec2 θ = 1 + tan2 θ.
Prove the following trigonometric identities.
`"cosec" theta sqrt(1 - cos^2 theta) = 1`
Prove the following identities:
(1 – tan A)2 + (1 + tan A)2 = 2 sec2A
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
`(1-tan^2 theta)/(cot^2-1) = tan^2 theta`
If `m = (cos θ - sin θ)` and `n = (cos θ + sin θ)`, show that `sqrt(m/n) + sqrt(n/m) = 2/sqrt(1 - tan^2θ)`.
Write the value of `(sin^2 theta 1/(1+tan^2 theta))`.
If sin θ = `11/61`, find the values of cos θ using trigonometric identity.
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`
Prove the following identity :
`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`
Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.
If `tan θ = 9/40`, complete the activity to find the value of sec θ.
Activity:
sec2θ = 1 + `square` ...[Fundamental trigonometric identity]
sec2θ = 1 + `square^2`
sec2θ = 1 + `square`
sec θ = `square`
If cos (α + β) = 0, then sin (α – β) can be reduced to ______.
If cosA + cos2A = 1, then sin2A + sin4A = 1.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
sec θ when expressed in term of cot θ, is equal to ______.
