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प्रश्न
If `1 - cos^2θ = 1/4`, then θ = ?
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उत्तर
`1 - cos^2θ = 1/4` ...[Given]
∴ `sin^2θ = 1/4` ...`[(∵ sin^2θ + cos^2θ = 1),(∴ 1 - cos^2θ = sin^2θ)]`
∴ `sin θ = 1/2` ...[Taking square root of both sides]
∴ θ = 30° ...`[∵ sin 30^circ = 1/2]`
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संबंधित प्रश्न
Prove the following trigonometric identities:
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`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`
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If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
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If `cos theta = 2/3 , " write the value of" (4+4 tan^2 theta).`
If 3 `cot theta = 4 , "write the value of" ((2 cos theta - sin theta))/(( 4 cos theta - sin theta))`
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If tan A + sin A = m and tan A − sin A = n, then show that `m^2 - n^2 = 4 sqrt (mn)`.
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Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
