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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

5sin2θ-5cot2θ, complete the activity given below. Activity: 5sin2θ-5cot2θ = □(1sin2θ-cot2θ) = 5(□-cot2θ) ......[1sin2θ=□] = 5(1) = □ - Geometry Mathematics 2

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प्रश्न

`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.

Activity:

`5/(sin^2theta) - 5cot^2theta`

= `square (1/(sin^2theta) - cot^2theta)`

= `5(square - cot^2theta)   ......[1/(sin^2theta) = square]`

= 5(1)

= `square`

रिकाम्या जागा भरा
बेरीज

उत्तर

`5/(sin^2theta) - 5cot^2theta`

= `5 (1/(sin^2theta) - cot^2theta)`

= `5("cosec"^2theta - cot^2theta)   ......[1/(sin^2theta) = "cosec"^2theta]`

= 5(1)

= 5.

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पाठ 6: Trigonometry - Q.2 (A)

संबंधित प्रश्‍न

Express the ratios cos A, tan A and sec A in terms of sin A.


Prove the following trigonometric identities.

`(cos^2 theta)/sin theta - cosec theta +  sin theta  = 0`


Prove that

`sqrt((1 + sin θ)/(1 - sin θ)) + sqrt((1 - sin θ)/(1 + sin θ)) = 2 sec θ`


Prove the following identities:

`((1 + tan^2A)cotA)/(cosec^2A) = tan A`


Prove that:

(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A


`tan theta /((1 - cot theta )) + cot theta /((1 - tan theta)) = (1+ sec theta cosec  theta)`


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


If sec θ + tan θ = x, write the value of sec θ − tan θ in terms of x.


The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is 


Prove the following identity : 

`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`


Prove the following identity : 

`(1 + tan^2θ)sinθcosθ = tanθ`


For ΔABC , prove that : 

`sin((A + B)/2) = cos"C/2`


There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.


Prove the following identities.

`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec"  theta - 1)/("cosec"  theta + 1)`


If tan θ + cot θ = 2, then tan2θ + cot2θ = ?


If 1 + sin2α = 3 sinα cosα, then values of cot α are ______.


If cosec θ + cot θ = p, then prove that cos θ = `(p^2 - 1)/(p^2 + 1)`


Complete the following activity to prove:

cotθ + tanθ = cosecθ × secθ

Activity: L.H.S. = cotθ + tanθ

= `cosθ/sinθ + square/cosθ`

= `(square + sin^2theta)/(sinθ xx cosθ)`

= `1/(sinθ xx  cosθ)` ....... ∵ `square`

= `1/sinθ xx 1/cosθ`

= `square xx secθ`

∴ L.H.S. = R.H.S.


Show that: `tan "A"/(1 + tan^2 "A")^2 + cot "A"/(1 + cot^2 "A")^2 = sin"A" xx cos"A"`


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