prove tan(-a)=-tan(a)

Solution

prove

tan (- a) = - tan (a)

True

Solution steps

tan (- a) = - tan (a)

Manipulating left side

tan (- a)

Use the negative angle identity:

tan (- x) = - tan (x)

= - tan (a)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( y ) + cos ( y )}{1 + sin ( y )} = sec (y)

sin^{2} (x) + cos (2 x) = 1 - sin^{2} (x)

cos (4 5^{\circ}) = \frac{sin ( 2 \cdot 4 5 ^{\circ} )}{2 \cdot sin ( 4 5 ^{\circ} )}

4 sin (3 x) cos (4 x) = 2 sin (7 x) - 2 sin (x)

sec^{2} (x) = \frac{sec ( x )}{cos ( x )}