मराठी

Write the Value Of`(Tan^2 Theta - Sec^2 Theta)/(Cot^2 Theta - Cosec^2 Theta)`

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प्रश्न

Write the value of`(tan^2 theta  - sec^2 theta)/(cot^2 theta - cosec^2 theta)`

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उत्तर

`(tan^2 theta - sec^2 theta )/ (cot^2 theta - cosec^2 theta)`

  =` (-1)/(-1)`

  = 1

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पाठ 13: Trigonometric identities - Exercises 3

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आर. एस. अग्रवाल Mathematics [English] Class 10
पाठ 13 Trigonometric identities
Exercises 3 | Q 15

संबंधित प्रश्‍न

Prove that:

sec2θ + cosec2θ = sec2θ x cosec2θ


Prove the following trigonometric identities:

(i) (1 – sin2θ) sec2θ = 1

(ii) cos2θ (1 + tan2θ) = 1


Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`


Prove that `cosA/(1+sinA) + tan A =  secA`


Prove the following trigonometric identities.

sec A (1 − sin A) (sec A + tan A) = 1


Prove the following identities:

`cosecA + cotA = 1/(cosecA - cotA)`


Prove that:

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


Prove the following identities:

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


If`( 2 sin theta + 3 cos theta) =2 , " prove that " (3 sin theta - 2 cos theta) = +- 3.`


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


If `secθ = 25/7 ` then find tanθ.


Prove the following identity : 

`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`


Prove the following identity : 

`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`


prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`


If sin θ = `1/2`, then find the value of θ. 


If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.


`(1 - tan^2 45^circ)/(1 + tan^2 45^circ)` = ?


tan2θ – sin2θ = tan2θ × sin2θ. For proof of this complete the activity given below.

Activity:

L.H.S. = `square`

= `square (1 - (sin^2θ)/(tan^2θ))`

= `tan^2θ (1 - square/((sin^2θ)/(cos^2θ)))`

= `tan^2θ (1 - (sin^2θ)/1 xx (cos^2θ)/square)`

= `tan^2θ (1 - square)`

= `tan^2θ xx square`   ...[1 – cos2θ = sin2θ]

= R.H.S.


Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.


Factorize: sin3θ + cos3θ

Hence, prove the following identity:

`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`


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