Is tan((4pi)/3-pi/4)=2-sqrt(3) ?

The answer to whether tan((4pi)/3-pi/4)=2-sqrt(3) is True

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prove tan((4pi)/3-pi/4)=2-sqrt(3)

prove

tan (\frac{4 π}{3} - \frac{π}{4}) = 2 - 3

True

Solution steps

tan (\frac{4 π}{3} - \frac{π}{4}) = 2 - 3

Manipulating left side

tan (\frac{4 π}{3} - \frac{π}{4})

Rewrite using trig identities

= 2 - 3

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

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

sec^{2} (x) = \frac{2}{( 1 + cos ^{2} ( x ) )}

Is tan((4pi)/3-pi/4)=2-sqrt(3) ?
The answer to whether tan((4pi)/3-pi/4)=2-sqrt(3) is True