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`(1+ Cos Theta - Sin^2 Theta )/(Sin Theta (1+ Cos Theta))= Cot Theta` - Mathematics

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

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

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

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

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

     =`cos theta/ sin theta`

     = cot ЁЭЬГ
     = RHS
Hence, L.H.S. = R.H.S.

  

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рдкрд╛рда 8: Trigonometric Identities - Exercises 1

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Prove the following trigonometric identities.

`tan A/(1 + tan^2  A)^2 + cot A/((1 + cot^2 A)) = sin A  cos A`


Prove that

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


Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)

Show that one of the values of each member of this equality is sin α sin β sin γ


Prove the following identities:

`1/(1 - sinA) + 1/(1 + sinA) = 2sec^2A`


Prove that:

(sec A − tan A)2 (1 + sin A) = (1 − sin A)


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


If `cos B = 3/5 and (A + B) =- 90° ,`find the value of sin A.


Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\] 


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


If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.


\[\frac{1 + \tan^2 A}{1 + \cot^2 A}\]is equal to


Prove the following identity : 

`(cosecθ)/(tanθ + cotθ) = cosθ`


Find A if tan 2A = cot (A-24°).


Prove that `(tan^2"A")/(tan^2 "A"-1) + (cosec^2"A")/(sec^2"A"-cosec^2"A") = (1)/(1-2 co^2 "A")`


Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.


If A + B = 90°, show that sec2 A + sec2 B = sec2 A. sec2 B.


Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.


Prove the following identities.

cot θ + tan θ = sec θ cosec θ


Choose the correct alternative:

Which is not correct formula?


Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?


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