Question

If theta= 45degree, verify Sin 2theta=2Sin theta*Cos theta

Answer 1

theta = 45 degrees

hence prove; sin 2x45 = 2 sin 45 x cos 45

LHS:

sin 90 = 1

RHS:

2 (1/√2) x (1/√2)

= (2/√2) x (1/√2)

= 2/2

= 1

hence proved

Answer 2

Answer: we can verify this sum by first solving the left hand side that is sin2 theta.

So, sin2 theta is equal to sin2(45) as theta is 45 as given in the sum...

Therefore sin2 theta = sin 90

Where sin 90 is 1

So left hand side 's ans is 1

Now solving the right hand side, ie.

2sin theta × cos theta which is equal to :

2sin45 × cos 45

Where sin 45 is one by root 2 and cos 45 is also one by root 2

Therefore substituting the value,

2 × one by root 2 × one by root 2

Which gives the answer 1 as one by root 2 nd one by root 2 combine together to form half and when 2 and half are multiplied, 2 in the numerator and 2 in the denominator gets canceled leaving the answer as one which matches the answer of the left hand side

Therefore Lhs =Rhs

Hence verified