Question

Let A = 45°. Verify each of the following
53. sin 2A = 2 sin A cos A​

Answer 1

Answer:

Step-by-step explanation:

Given to verify : sin 2A = 2 sin A cos A

If A = 45°

sin2A = sin(2*45) = sin90 = 1 [ T - Ratio of 90° , π/2 ]

sinA = sin45 = 1/√2 [ T - Ratio of 45° , π/4 ]

cosA = cos45 = 1/√2 [ T - Ratio of 45° , π/4 ]

Now,

Given equation to verify : sin 2A = 2 sin A cos A

Finding the value of Left Hand Side ( L. H. S)

= sin2A

= sin90

= 1

Finding the value of Right Hand side [ R. H. S ]

= 2 sinA * cosA

= 2 ( 1/√2)(1/√2)

= √2/√2

= 1 .

Here, We observe that L. H. S = R. H. S.

Hence proved that, sin2A = 2sinA cosA for A = 45°

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Answer 2

Answer:

sin2A=2sinA cosA

sin 90°=2 sin45°*cos45°

1=2*1/√2*1/√2

1=2*1/2

1=1

LHS=RHS

HENCE VERIFIED.........