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प्रश्न
If 3 sin θ = 4 cos θ, then sec θ = ?
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उत्तर
3 sin θ = 4 cos θ ...[Given]
∴ `(sin θ)/(cos θ) = 4/3`
∴ `tan θ = 4/3`
We know that,
1 + tan2θ = sec2θ
∴ `1 + (4/3)^2 = sec^2θ`
∴ `1 + 16/9 = sec^2θ`
∴ `sec^2θ = (9 + 16)/9`
∴ `sec^2θ = 25/9`
∴ `sec θ = 5/3` ...[Taking square root of both sides]
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संबंधित प्रश्न
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
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Prove the following trigonometric identities.
`(cot A - cos A)/(cot A + cos A) = (cosec A - 1)/(cosec A + 1)`
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p2 – 1) = 2p.
Prove that:
`cot^2A/(cosecA - 1) - 1 = cosecA`
Prove that
`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
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If 5x = sec θ and \[\frac{5}{x} = \tan \theta\]find the value of \[5\left( x^2 - \frac{1}{x^2} \right)\]
Prove the following identity :
`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`
Prove that sin θ sin( 90° - θ) - cos θ cos( 90° - θ) = 0
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
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Which is not correct formula?
`5/(sin^2θ) - 5cot^2θ`, complete the activity given below.
Activity:
`5/(sin^2θ) - 5cot^2θ`
= `square (1/(sin^2θ) - cot^2θ)`
= `5(square - cot^2θ) ...[1/(sin^2θ) = square]`
= 5(1)
= `square`
Prove that sec2θ – cos2θ = tan2θ + sin2θ.
If 1 + sin2θ = 3 sin θ cos θ, then prove that tan θ = 1 or `1/2`.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
Statement 1: sin2θ + cos2θ = 1
Statement 2: cosec2θ + cot2θ = 1
Which of the following is valid?
