Question

If x= tanA + sinA and y= tan A-sin A,proove that : ( x+y/x-y) 2 -( x+y/2) 2 =1

Answer 1

Given: x = tanA + sinA and y = tanA – sinA

Therefore,

x + y = tanA + sinA + tanA – sinA = 2 tanA

x – y = tanA + sinA – tanA + sinA = 2 sinA

LHS = (x+y/x-y)2 – (x+y/2)2

Substitute the value of x+y  and  x-y

LHS = (2 tanA /2 sinA)2 – (2 tanA/2)2

        = ((sinA/cosA)/sinA)2 – tan2A

         = (1/cosA)2 – tan2A

         = sec2A – tan2A

         = 1 + tan2A – tan2A

          = 1

         = RHS

Hence proved.

Answer 2

Answer:

( x+y/x-y) 2 -( x+y/2) 2 =1

Step-by-step explanation:

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