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Write the Value of `Cosec^2 Theta (1+ Cos Theta ) (1- Cos Theta).` - Mathematics

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प्रश्न

Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`

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उत्तर

`cosec^2 theta (1+ cos theta )(1- cos theta)`

       = `cosec^2 theta (1- cos^2 theta)`

       =`1/ sin^2 theta xx sin^2 theta `

       = 1

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अध्याय 8: Trigonometric Identities - Exercises 3

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आर.एस. अग्रवाल Mathematics [English] Class 10
अध्याय 8 Trigonometric Identities
Exercises 3 | Q 10

संबंधित प्रश्न

Prove the following trigonometric identities:

`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `


Prove that `(sin theta)/(1-cottheta) + (cos theta)/(1 - tan theta) = cos theta + sin theta`


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`(1 - cos^2 A) cosec^2 A = 1`


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Prove the following identities:

(1 – tan A)2 + (1 + tan A)2 = 2 sec2A


Prove the following identities:

sec2A + cosec2A = sec2A . cosec2A


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`1/(sinA - cosA) - 1/(sinA + cosA) = (2cosA)/(2sin^2A - 1)`


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Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`


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\[\frac{\tan \theta}{\sec \theta - 1} + \frac{\tan \theta}{\sec \theta + 1}\] is equal to 

 

 


If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2


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`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`


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`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`


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