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

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prove sin(2x)=2sin(x)

Solution

prove

sin (2 x) = 2 sin (x)

False

Solution steps

sin (2 x) = 2 sin (x)

Show that the two sides are not equal

For

sin (2 x) = 2 sin (x)

plug in

x = 1

sin (2 \cdot 1) = 0.90929 \dots

sin (2 \cdot 1)

Refine to a decimal form

= 0.90929 \dots

2 sin (1) = 1.68294 \dots

2 sin (1)

Refine to a decimal form

= 1.68294 \dots

The two sides are not equal

\Rightarrow False

\frac{sec ^{2} ( x ) - 1}{sec ( x ) - 1} = sec (x) + 1

sin (θ) - cos^{2} (θ) = sin^{3} (θ)

csc^{4} (θ) = cot^{4} (θ) + 2 cot^{2} (θ) + 1

sec (x + y) = \frac{sec ( x ) sec ( y ) csc ( x ) csc ( y )}{csc ( x ) csc ( y ) - sec ( x ) sec ( y )}

1 - tan^{2} (a) = cos (2 a) sec^{2} (a)