What is 2cos^2(3x-pi/4)-1 ?

The solution to 2cos^2(3x-pi/4)-1 is ((sqrt(2)cos(3x)+sqrt(2)sin(3x))^2)/2-1

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simplify 2cos^2(3x-pi/4)-1

simplify

2 cos^{2} (3 x - \frac{π}{4}) - 1

\frac{( 2 cos ( 3 x ) + 2 sin ( 3 x ) ) ^{2}}{2} - 1

Solution steps

2 cos^{2} (3 x - \frac{π}{4}) - 1

Rewrite using trig identities

= 2 (\frac{2 cos ( 3 x ) + 2 sin ( 3 x )}{2})^{2} - 1

2 (\frac{2 cos ( 3 x ) + 2 sin ( 3 x )}{2})^{2} = \frac{( 2 cos ( 3 x ) + 2 sin ( 3 x ) ) ^{2}}{2}

= \frac{( 2 cos ( 3 x ) + 2 sin ( 3 x ) ) ^{2}}{2} - 1

cos (πn) - cos (- πn)

\frac{10 m}{sin ( 4 0 ^{\circ} )}

cos (36 0^{\circ} - a)

cos (- x^{2})

cos (arctan (\frac{x}{7}))

What is 2cos^2(3x-pi/4)-1 ?
The solution to 2cos^2(3x-pi/4)-1 is ((sqrt(2)cos(3x)+sqrt(2)sin(3x))^2)/2-1