What is (tan(x+45))^2 ?

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

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simplify (tan(x+45))^2

simplify

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

\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 )}

- sin (x - 2 x)

3 cos (x + \frac{π}{2}) - 1

cot (arcsin (\frac{w - 1}{w + 2}))

cos ((\frac{5 π}{2}) + θ)

sin (6 0^{\circ} - a)

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