Is sin(40)=2sin(20)cos(20) ?

The answer to whether sin(40)=2sin(20)cos(20) is True

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prove sin(40)=2sin(20)cos(20)

prove

sin (4 0^{\circ}) = 2 sin (2 0^{\circ}) cos (2 0^{\circ})

True

Solution steps

sin (4 0^{\circ}) = 2 sin (2 0^{\circ}) cos (2 0^{\circ})

Manipulating left side

sin (4 0^{\circ})

Rewrite using trig identities

sin (4 0^{\circ})

= sin (2 \cdot 2 0^{\circ})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (2 0^{\circ}) cos (2 0^{\circ})

= 2 sin (2 0^{\circ}) cos (2 0^{\circ})

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) - cos^{2} (θ) sin (θ) = sin^{3} (θ)

\frac{9}{sec ( x ) + 1} - \frac{9}{sec ( x ) - 1} = 0

sec^{2} (x) + csc^{2} (x) = (sec (x) csc (x))^{2}

tan (x) = \frac{sin ( x ) csc ( x )}{cot ( x )}

tan (x) sec (x) cos (x) = tan (x)

Is sin(40)=2sin(20)cos(20) ?
The answer to whether sin(40)=2sin(20)cos(20) is True