What is sec^2(pi/4+x) ?

The solution to sec^2(pi/4+x) is 2/(1-sin(2x))

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simplify sec^2(pi/4+x)

simplify

sec^{2} (\frac{π}{4} + x)

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

Solution steps

sec^{2} (\frac{π}{4} + x)

Rewrite using trig identities

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

Simplify

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

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

Expand

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

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

Rewrite using trig identities

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

cot (5 x - \frac{5 π}{3})

cos (\frac{nπ \cdot 2}{2})

- 6 sin (ω t - \frac{π}{4})

csc (- cos (\cdot cot (x)))

cos (arctan (7 x^{3}))