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

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

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ЁЭР┐ЁЭР╗ЁЭСЖ = `(tan theta)/(1+tan^2 theta )^2 +( cot theta )/(1+cot^2 theta)^2`

        =`tan theta/ ((sec^2  theta)^2) + cot theta/((cosec^2  theta) ^2)`

        =`tan theta / sec^4 theta + cottheta/(cosec^4  theta)`

        =`sin theta/cos theta xx cos^4 theta + cos theta/sin theta xx sin ^4 theta`

      =` sin  theta  cos  ^3 theta + cos theta sin  ^3 theta`

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

    =`sin theta cos theta`

    = RHS

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рдЕрдзреНрдпрд╛рдп 8: Trigonometric Identities - Exercises 1

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рдЖрд░рдПрд╕ рдЕрдЧреНрд░рд╡рд╛рд▓ Mathematics [English] Class 10
рдЕрдзреНрдпрд╛рдп 8 Trigonometric Identities
Exercises 1 | Q 16

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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}`


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


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


Prove the following trigonometric identities.

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


Prove the following trigonometric identities.

if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`


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


(cosec θ − sin θ) (sec θ − cos θ) (tan θ + cot θ) is equal to


Prove the following identity : 

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


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


Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A


Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.


Prove that: `sqrt((1 - cos θ)/(1 + cos θ)) = cosec θ - cot θ`.


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


If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `±  sqrt("a"^2 + "b"^2 -"c"^2)`


If tan θ = `13/12`, then cot θ = ?


If sec θ = `41/40`, then find values of sin θ, cot θ, cosec θ


Prove that `"cot A"/(1 - tan "A") + "tan A"/(1 - cot"A")` = 1 + tan A + cot A = sec A . cosec A + 1


`sqrt((1 - cos^2theta) sec^2 theta) = tan theta` 


Show that `(cos^2(45^circ + theta) + cos^2(45^circ - theta))/(tan(60^circ + theta) tan(30^circ - theta))` = 1


If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.


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