What is tan^2(x+45) ?

The solution to tan^2(x+45) is (1+sin(2x))/(1-sin(2x))

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simplify tan^2(x+45)

simplify

tan^{2} (x + 4 5^{\circ})

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

Solution steps

tan^{2} (x + 4 5^{\circ})

Rewrite using trig identities

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Expand

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

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

Rewrite using trig identities

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

cos (9 0^{\circ} - x) - sin (x)

sin (\frac{3 π}{2} - A)

cos (10 π - x)

sin (2 π \cdot 1 \cdot t - 0.25 π)

cot (- 1 (n + 1) - cot (- 1 (n)))