Question

Prove that sin2x=2sin(x) cos (x)​

Answer 1

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Prove that $\sf \sin2x = 2 \sin(x) \cos(x)$

$\star\:\:\:\sf\large\underline\blue{Proof:-}$

We know that,

$\sf\sin( x + y) = \sin(x) \cos(y) + \sin(y) \cos(x)$

Here,

$\sf \sin(2x)$

$\sf = \sin(x + x)$

$\sf = \sin(x) \cos(x) + \sin(x) \cos(x)$

$\sf = 2 \sin(x) \cos(x)$

Therefore,

$\boxed{ \sf \sin(2x) = 2 \sin(x) \cos(x) }$

Hence Proved.

Answer 2

Answer:

$\huge{ \bold{ \boxed{ \mathtt{ \green{answer}{} }{} }{} }{} }{}$

»Question

• Prove that sin2x=2sin(x) cos (x)

»Answer:-

»Given:-

• Prove that sin2x=2sin(x) cos (x)

To prove:-

★Prove that sin2x=2sin(x) cos (x)

Step-by-step explanation:

$\bold{ \red{solution}{} }{}$

$\sin(2x) = \: \sin(x + x) \\ \\ = > \sin(2x) = \: \sin(x) \cos(x) + \sin(x) \cos(x) ........ \\ \\ = > \sin(A + B) = \: \sin(A) \cos(B) + \sin(B) \\ \\ \bold{ \green{hence \: \sin(2x = \2sin(x) \cos(x) ) ) }{} }{}$

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