Is sin(20)=2cos(10)*sin(10) ?

The answer to whether sin(20)=2cos(10)*sin(10) is True

prove sin(20)=2cos(10)*sin(10)

prove

sin (2 0^{\circ}) = 2 cos (1 0^{\circ}) \cdot sin (1 0^{\circ})

True

Solution steps

sin (2 0^{\circ}) = 2 cos (1 0^{\circ}) sin (1 0^{\circ})

Manipulating left side

sin (2 0^{\circ})

Rewrite using trig identities

sin (2 0^{\circ})

= sin (2 \cdot 1 0^{\circ})

Use the Double Angle identity:

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

= 2 sin (1 0^{\circ}) cos (1 0^{\circ})

= 2 sin (1 0^{\circ}) cos (1 0^{\circ})

= 2 cos (1 0^{\circ}) sin (1 0^{\circ})

We showed that the two sides could take the same form

\Rightarrow True

p ro v e sin^{2} (x) = sec (x) cos (x) - cos^{2} (x)

p ro v e 1 - 2 sin^{2} (2 θ) = 8 cos^{4} (θ) - 8 cos^{2} (θ) + 1

p ro v e sech^{2} (x) + tanh^{2} (x) = 1

p ro v e 2 cos^{2} (A) - cos (2 A) - 1 = 0

p ro v e \frac{cot ( x ) + 1}{cos ( x ) + sin ( x )} = csc (x)

Is sin(20)=2cos(10)*sin(10) ?
The answer to whether sin(20)=2cos(10)*sin(10) is True