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` Tan^2 Theta - 1/( Cos^2 Theta )=-1` - Mathematics

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प्रश्न

` tan^2 theta - 1/( cos^2 theta )=-1`

उत्तर

LHS= `tan^2 theta - 1/(cos^2 theta)`

    =` (sin^2 theta )/( cos^2 theta) - 1/(cos^2 theta)`

    =`(sin ^2 theta-1)/(cos^2 theta)`

   =` (-cos^2 theta )/(cos^2 theta)`

   =  -1

  = RHS

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पाठ 8: Trigonometric Identities - Exercises 1

APPEARS IN

आर एस अग्रवाल Mathematics [English] Class 10
पाठ 8 Trigonometric Identities
Exercises 1 | Q 5.2

संबंधित प्रश्‍न

Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`


Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

if x = a cos^3 theta, y = b sin^3 theta` " prove that " `(x/a)^(2/3) + (y/b)^(2/3) = 1`


Prove the following identities:

cosecA – cosec2 A = cot4 A + cot2 A


Prove the following identities:

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


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

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


`1+ (cot^2 theta)/((1+ cosec theta))= cosec theta`


If `sqrt(3) sin theta = cos theta  and theta ` is an acute angle, find the value of θ .


Prove that:

`"tan A"/(1 + "tan"^2 "A")^2 + "Cot A"/(1 + "Cot"^2 "A")^2 = "sin A cos A"`.


The value of sin2 29° + sin2 61° is


If a cos θ − b sin θ = c, then a sin θ + b cos θ =


Prove the following identity : 

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


Prove the following identity :

`sec^2A + cosec^2A = sec^2Acosec^2A`


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.


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`(cos 70°)/(sin 20°) + (cos 59°)/(sin 31°) - 8sin^2 30° = 0`.


Prove that `(sin 70°)/(cos 20°) + (cosec 20°)/(sec 70°) - 2 cos 70° xx cosec 20°` = 0.


Choose the correct alternative:

1 + cot2θ = ? 


Prove that cot2θ – tan2θ = cosec2θ – sec2θ 


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.


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