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प्रश्न
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
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उत्तर
LHS = `cos^2 A + 1/(cosec^2 A)`
= cos2 A + sin2 A
= 1
= RHS
Hence proved.
संबंधित प्रश्न
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 identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
Prove the following identities:
`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`
If x=a `cos^3 theta and y = b sin ^3 theta ," prove that " (x/a)^(2/3) + ( y/b)^(2/3) = 1.`
If sec θ + tan θ = x, then sec θ =
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Find the value of ( sin2 33° + sin2 57°).
If sin θ = `1/2`, then find the value of θ.
tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.
Activity:
L.H.S = `square`
= `square (1 - (sin^2theta)/(tan^2theta))`
= `tan^2theta (1 - square/((sin^2theta)/(cos^2theta)))`
= `tan^2theta (1 - (sin^2theta)/1 xx (cos^2theta)/square)`
= `tan^2theta (1 - square)`
= `tan^2theta xx square` .....[1 – cos2θ = sin2θ]
= R.H.S
If cos A + cos2A = 1, then sin2A + sin4 A = ?
