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प्रश्न
The value of \[\sqrt{\frac{1 + \cos \theta}{1 - \cos \theta}}\]
पर्याय
cot θ − cosec θ
cosec θ + cot θ
cosec2 θ + cot2 θ
(cot θ + cosec θ)2
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`
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संबंधित प्रश्न
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Without using trigonometric identity , show that :
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Show that, cotθ + tanθ = cosecθ × secθ
Solution :
L.H.S. = cotθ + tanθ
= `cosθ/sinθ + sinθ/cosθ`
= `(square + square)/(sinθ xx cosθ)`
= `1/(sinθ xx cosθ)` ............... `square`
= `1/sinθ xx 1/square`
= cosecθ × secθ
L.H.S. = R.H.S
∴ cotθ + tanθ = cosecθ × secθ
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
