Is sin(2x)+cos(2x)=1+2sin(x)cos(x) ?

The answer to whether sin(2x)+cos(2x)=1+2sin(x)cos(x) is False

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prove sin(2x)+cos(2x)=1+2sin(x)cos(x)

prove

sin (2 x) + cos (2 x) = 1 + 2 sin (x) cos (x)

False

Solution steps

sin (2 x) + cos (2 x) = 1 + 2 sin (x) cos (x)

Show that the two sides are not equal

For

sin (2 x) + cos (2 x) = 1 + 2 sin (x) cos (x)

plug in

x = 1

sin (2 \cdot 1) + cos (2 \cdot 1) = 0.49315 \dots

sin (2 \cdot 1) + cos (2 \cdot 1)

Refine to a decimal form

= 0.49315 \dots

1 + 2 sin (1) cos (1) = 1.90929 \dots

1 + 2 sin (1) cos (1)

Refine to a decimal form

= 1.90929 \dots

The two sides are not equal

\Rightarrow False

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Is sin(2x)+cos(2x)=1+2sin(x)cos(x) ?
The answer to whether sin(2x)+cos(2x)=1+2sin(x)cos(x) is False