Is 2sin(-t)cos(-t)=2sin(-t)cos(t) ?

The answer to whether 2sin(-t)cos(-t)=2sin(-t)cos(t) is True

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prove 2sin(-t)cos(-t)=2sin(-t)cos(t)

prove

2 sin (- t) cos (- t) = 2 sin (- t) cos (t)

True

Solution steps

2 sin (- t) cos (- t) = 2 sin (- t) cos (t)

Manipulating left side

2 sin (- t) cos (- t)

Use the negative angle identity:

sin (- x) = - sin (x)

= 2 cos (- t) (- sin (t))

Use the negative angle identity:

cos (- x) = cos (x)

= 2 cos (t) (- sin (t))

Manipulating right side

2 sin (- t) cos (t)

Use the negative angle identity:

sin (- x) = - sin (x)

= 2 cos (t) (- sin (t))

We showed that the two sides could take the same form

\Rightarrow True

2 tan^{2} (x) = \frac{2 sin ^{2} ( x )}{cos ^{2} ( x )}

csc (θ) \cdot tan (θ) = sec (θ)

cot (θ) \cdot csc (θ) \cdot sec (θ) = csc^{2} (θ)

sin (x) + cos (x) + cot (x) = csc (x)

sin^{2} (α) + sin^{2} (α) tan^{2} (α) = tan^{2} (α)

Is 2sin(-t)cos(-t)=2sin(-t)cos(t) ?
The answer to whether 2sin(-t)cos(-t)=2sin(-t)cos(t) is True