prove that:   sinA/tanA + cosA = 2cosA

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

sinA / tanA + cosA = 2cosA

We will start from the left side:

We know that tanA = sinA/cosA

Now substitute:

sinA/ tanA + cosA = sinA/(sinA/cosA)  + cosA

                             = (sinA*cosA / sinA)   + cosA

                             = cosA + cosA

                              = 2cosA

==> sinA/tanA + cosA = 2cosA

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To prove sinA/tanA+cosA = 2cosA

Solution:

Let  ABC be the right anled triangle with right angle at B.

Then  by definition, sinA = BC/AC, cos A =  AB/AC an d tan A = BC/AB.

SO LHS = sinA/tanA + cosA = ( BC/AC)/(BC/AB)+AB/AC = BC*AB/(AC*BC) +AB/AC = 2AB/AC+AB/AC = 2AB/AC = 2cosA = LHS.

THrefore sinA/tanA+cosA = 2cosA.

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