Question

If sin a + cos a = root (2) , then find value of sin2a

Answer 1

Hey there !!!!!


  sinA+cosA= √2-----Equation 1

Dividing equation 1 with √2 on both sides

sinA/√2+cosA/√2 =√2/√2----Equation 2

We know that  sin45=1/√2 and cos45=1/√2

So, Equation 2 changes to 

sinAcos45+cosAsin45=1-----Equation 3

LHS of equation 3 is of the form sinXcosY+cosXsinY=sin(X+Y)

So, X=A Y=45

sin(A+45)=1

But sin90=1

SO,

 sin(A+45)=sin90

A+45=90

A=90-45=45

sin2A=sin2*45=sin90 =1.

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Hope this helped you...........