prove tan(-pi/4)=-1

Solution

prove

tan (- \frac{π}{4}) = - 1

True

Solution steps

tan (- \frac{π}{4}) = - 1

Manipulating left side

tan (- \frac{π}{4})

Use the negative angle identity:

tan (- x) = - tan (x)

= - tan (\frac{π}{4})

Simplify

= - 1

We showed that the two sides could take the same form

\Rightarrow True

(cos (θ) - sin (θ))^{2} = 1 - sin (2 θ)

csc (x) sec (x) = 2 csc (2 x)

sin^{2} (x) = \frac{1}{1 + cot ^{2} ( x )}

2 sec^{2} (x) - 2 cot^{2} (\frac{π}{2} - x) = 2

(cos (x) - sin (x))^{2} = sec^{2} (x) - 2 tan (x)