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प्रश्न
`(1 + cot^2 theta ) sin^2 theta =1`
उत्तर
LHS= `(1+cot^2 theta)sin^2 theta`
=`cosec^2 theta sin^2 theta (∵ cosec^2 theta - cot^2 theta =1)`
=`1/(sin ^2theta)xxsin^2 theta`
=1
Hence, LHS = RHS
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संबंधित प्रश्न
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following identities:
`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`
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If `( cosec theta + cot theta ) =m and ( cosec theta - cot theta ) = n, ` show that mn = 1.
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`(sin^2θ)/(cosθ) + cosθ = secθ`
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
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`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
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If cot θ + tan θ = x and sec θ – cos θ = y, then prove that `(x^2y)^(2/3) – (xy^2)^(2/3)` = 1
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
If tan θ – sin2θ = cos2θ, then show that sin2 θ = `1/2`.
The value of 2sinθ can be `a + 1/a`, where a is a positive number, and a ≠ 1.
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If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
If tan θ = `x/y`, then cos θ is equal to ______.
