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`Sqrt((1-cos Theta)/(1+Cos Theta)) = (Cosec Theta - Cot Theta)` - Mathematics

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

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LHS = `sqrt((1-cos theta)/(1+ cos theta))`

      =`sqrt(((1-cos theta))/((1+cos theta)) xx ((1- cos theta))/((1 - cos theta))`

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

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

     =`(1-cos theta)/sin theta`

     =`1/sin theta - cos theta/ sin theta`

     =(ЁЭСРЁЭСЬЁЭСаЁЭСТЁЭСР ЁЭЬГ − cot ЁЭЬГ)
      = RHS

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рдкрд╛рда 8: Trigonometric Identities - Exercises 1

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Evaluate without using trigonometric tables:

`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`


Prove the following trigonometric identities.

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


If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that a2 + b2 = m2 + n2


Prove the following identities:

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


Prove the following identities:

`(1 - sinA)/(1 + sinA) = (secA - tanA)^2`


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`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`


Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`


`sin theta / ((1+costheta))+((1+costheta))/sin theta=2cosectheta` 


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


If 5x = sec ` theta and 5/x = tan theta , " find the value of 5 "( x^2 - 1/( x^2))`


Define an identity.


What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]


If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2. 


Prove the following identity :

`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`


Prove the following identity : 

`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`


Evaluate:

sin2 34° + sin56° + 2 tan 18° tan 72° – cot30°


Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.


Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`


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(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.


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