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Question

If sinA = 12 , verify that 2 sinA cosA = 2tanA(1+tan2A)


Solution

We know that 

  SinA = BCAC = 12

Let   BC = k and AC = 2k

∴      AB = AC2AB2  ......... (Pythagoras theorm )

               = (2k)2k2  = 4k2k2 = 3k2 = 3k

Now  cos A = ABAC  = 3k2k = 32 

and   tanA = BCABk3k = 13 

Now  2 sinA cosA = 2.123232     ......(i)

and  2tanA1+tan2A = 2.131+(13)2 = 2131+13  =  21343 

 = 23×34=32            ........... (ii)

Hence from (ii) and (i)

2 sinA cosA = 2tanA1+tan2A.


Mathematics

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