मराठी

If cosA + cos2A = 1, then sin2A + sin4A= 1. - Mathematics

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प्रश्न

If cosA + cos2A = 1, then sin2A + sin4A = 1.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

This statement is True.

Explanation:

∵ cosA + cos2A = 1

⇒ cosA = 1 – cos2A = sin2A  ...[∵ sin2A + cos2A = 1]

⇒ cos2A = sin4A

⇒ 1 – sin2A = sin4A  ...[∵ cos2A = 1 – sin2A]

⇒ sin2A + sin4A = 1

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Introduction To Trigonometry and Its Applications - Exercise 8.2 [पृष्ठ ९३]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 10
पाठ 8 Introduction To Trigonometry and Its Applications
Exercise 8.2 | Q 5 | पृष्ठ ९३

संबंधित प्रश्‍न

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`


Prove the following trigonometric identities

`cos theta/(1 - sin theta) = (1 + sin theta)/cos theta`


Prove the following trigonometric identities.

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


Prove that:

`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`


If sec A + tan A = p, show that:

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


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


If m = ` ( cos theta - sin theta ) and n = ( cos theta +  sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.


Write the value of `(sin^2 theta 1/(1+tan^2 theta))`. 


Write the value of `(cot^2 theta -  1/(sin^2 theta))`. 


If `cos theta = 2/3 , "write the value of" ((sec theta -1))/((sec theta +1))`


If 5 `tan theta = 4,"write the value of" ((cos theta - sintheta))/(( cos theta + sin theta))`


From the figure find the value of sinθ.


Prove that  `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`


If x = a tan θ and y = b sec θ then


Choose the correct alternative:

1 + cot2θ = ? 


Prove that cos2θ . (1 + tan2θ) = 1. Complete the activity given below.

Activity:

L.H.S = `square`

= `cos^2theta xx square    .....[1 + tan^2theta = square]`

= `(cos theta xx square)^2`

= 12

= 1

= R.H.S


If tan θ = `7/24`, then to find value of cos θ complete the activity given below.

Activity:

sec2θ = 1 + `square`    ......[Fundamental tri. identity]

sec2θ = 1 + `square^2`

sec2θ = 1 + `square/576`

sec2θ = `square/576`

sec θ = `square` 

cos θ = `square`     .......`[cos theta = 1/sectheta]`


To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.

Activity:

L.H.S = `square`

= `square/sintheta + sintheta/costheta`

= `(cos^2theta + sin^2theta)/square`

= `1/(sintheta*costheta)`     ......`[cos^2theta + sin^2theta = square]`

= `1/sintheta xx 1/square`

= `square`

= R.H.S


Prove the following:

`tanA/(1 + sec A) - tanA/(1 - sec A)` = 2cosec A


Prove that (sec θ + tan θ) (1 – sin θ) = cos θ


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