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`(Tan a + Tanb )/(Cot a + Cot B) = Tan a Tan B` - Mathematics

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`(tan A + tanB )/(cot A + cot B) = tan A tan B`

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LHS = `(tan A + tanB )/(cot A + cot B) `

       =`(tan A + tan B)/(1/ tan A + 1/ tanB)`

       =` (tan A + tan B)/( (tan A+tan B)/ (tan A tan B)`

        =`(tan A tan B ( tan A + tan B))/((tan A + tan B ))`

        = ЁЭСбЁЭСОЁЭСЫЁЭР┤ ЁЭСбЁЭСОЁЭСЫЁЭР╡
        = RHS
Hence, LHS = RHS

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рдкрд╛рда 8: Trigonometric Identities - Exercises 1

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Prove the following trigonometric identity.

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


Prove the following identities:

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


Prove the following identities:

`sinA/(1 + cosA) = cosec A - cot A`


Prove the following identities:

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


If sin A + cos A = m and sec A + cosec A = n, show that : n (m2 – 1) = 2 m


`sqrt((1+cos theta)/(1-cos theta)) + sqrt((1-cos theta )/(1+ cos theta )) = 2 cosec theta`

 


Write the value of ` sin^2 theta cos^2 theta (1+ tan^2 theta ) (1+ cot^2 theta).`


Find the value of ` ( sin 50°)/(cos 40°)+ (cosec 40°)/(sec 50°) - 4 cos 50°   cosec 40 °`


The value of sin2 29° + sin2 61° is


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


Prove the following identity :

`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ` 


Prove the following identities:

`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`


Prove the following identity : 

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`


If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)


Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`


Prove that  `sin^2 θ/ cos^2 θ + cos^2 θ/sin^2 θ = 1/(sin^2 θ. cos^2 θ) - 2`.


Prove the following identities.

`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ


a cot θ + b cosec θ = p and b cot θ + a cosec θ = q then p2 – q2 is equal to


Prove that `(cos^2theta)/(sintheta) + sintheta` = cosec θ


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


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