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प्रश्न
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
विकल्प
cot θ − cosec θ
cosec θ + cot θ
cosec2 θ + cot2 θ
(cot θ + cosec θ)2
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उत्तर
The given expression is `sqrt ((1+cosθ)/(1-cos θ))`
Multiplying both the numerator and denominator under the root by` (1+cosθ )`, we have
`sqrt (((1+cosθ)(1+cosθ))/((1+cosθ)(1-cos θ)))`
`=sqrt ((1+cosθ)^2/ ((1-cos^2 θ))`
`=sqrt((1+cos θ)^2/sin^2θ`
`=(1+cos θ)/(sinθ)`
= `1/sinθ+cosθ/sinθ`
= `cosecθ+cotθ`
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
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`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
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sec2A + cosec2A = sec2A . cosec2A
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Activity:
L.H.S. = `square`
= `square (1 - (sin^2θ)/(tan^2θ))`
= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`
= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`
= `tan^2θ (1 - square)`
= `tan^2θ xx square` ...[1 – cos2θ = sin2θ]
= R.H.S.
sin(45° + θ) – cos(45° – θ) is equal to ______.
If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 – 1) = 2p.
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