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`(1 + Cot^2 Theta ) Sin^2 Theta =1` - Mathematics

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प्रश्न

`(1 + cot^2 theta ) sin^2 theta =1`

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उत्तर

LHS= `(1+cot^2 theta)sin^2 theta`

      =`cosec^2 theta   sin^2 theta    (∵ cosec^2 theta - cot^2 theta =1)`

     =`1/(sin ^2theta)xxsin^2 theta`

    =1

Hence, LHS = RHS

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अध्याय 8: Trigonometric Identities - Exercises 1

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आर.एस. अग्रवाल Mathematics [English] Class 10
अध्याय 8 Trigonometric Identities
Exercises 1 | Q 1.2

संबंधित प्रश्न

Prove the following trigonometric identities.

`(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`


Prove the following trigonometric identities.

`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`


Prove that  `(sec theta - 1)/(sec theta + 1) = ((sin theta)/(1 + cos theta))^2` 


Prove the following identities:

`tan A - cot A = (1 - 2cos^2A)/(sin A cos A)`


Prove the following identities:

`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`


`sec theta (1- sin theta )( sec theta + tan theta )=1`


`(cos^3 theta +sin^3 theta)/(cos theta + sin theta) + (cos ^3 theta - sin^3 theta)/(cos theta - sin theta) = 2`


If \[\sin \theta = \frac{4}{5}\] what is the value of cotθ + cosecθ? 


 Write True' or False' and justify your answer  the following : 

The value of  \[\cos^2 23 - \sin^2 67\]  is positive . 


Prove that: 
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1


Prove the following identity :

sinθcotθ + sinθcosecθ = 1 + cosθ  


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`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`


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`(cosecA)/(cotA+tanA)=cosA`


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sin4A – cos4A = 1 – 2cos2A. For proof of this complete the activity given below.

Activity:

L.H.S = `square`

 = (sin2A + cos2A) `(square)`

= `1 (square)`       .....`[sin^2"A" + square = 1]`

= `square` – cos2A    .....[sin2A = 1 – cos2A]

= `square`

= R.H.S


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Prove the following identity:

(sin2θ – 1)(tan2θ + 1) + 1 = 0


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