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

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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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рдЕрдзреНрдпрд╛рдп 13: Trigonometric identities - Exercises 1

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рдЖрд░.рдПрд╕. рдЕрдЧреНрд░рд╡рд╛рд▓ Mathematics [English] Class 10
рдЕрдзреНрдпрд╛рдп 13 Trigonometric identities
Exercises 1 | Q 35

рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди

Prove the following trigonometric identities

(1 + cot2 A) sin2 A = 1


Prove the following trigonometric identities.

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


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:

(cos A + sin A)2 + (cos A – sin A)2 = 2


Prove the following identities:

sec2 A . cosec2 A = tan2 A + cot2 A + 2


Prove that:

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


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


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


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


`If sin theta = cos( theta - 45° ),where   theta   " is   acute, find the value of "theta` .


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


Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:

sin θ × cosec θ = ______


If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2?


(sec A + tan A) (1 − sin A) = ______.


Prove the following identity :

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


Prove the following identity : 

`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`


Prove that  `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`


Prove the following identities:

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


Prove that `1/("cosec"  θ - cot θ) = "cosec"  θ + cot θ`.


If 3 sin θ = 4 cos θ, then sec θ = ?


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