Question

Prove that (cosA/1-tanA) + (sinA/1-cotA) = cosA+sinA

Answer 1

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prove the following identity- cosA/(1-tanA)+sinA/(1-cotA)=cosA+sinA

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HALA718  | CERTIFIED EDUCATOR

cosA/ (1-tanA) - sinA/(1-cotA) = cosA + sinA

We know that:

tanA = sinA/cosA

cotA = cosA/sinA

Now substitute in L.H.S:

==> cosA/(1-sinA/cosA)  -  sinA/(1-cosA/sinA)

   = cosA/[(cosA-sinA)/cosA] - sinA/[(sinA-cosA)/sinA]

   = (cos^2 A - sin^2 A)/ (cosA-sinA)

 =  (cosA-sinA)(cosA+ sinA)/(cosA-sinA)

= cosA + sinA  = R.H.S

Answer 2

Step-by-step explanation:

see the attachment above