What is the general solution for y=cos^{215}(0)-sin^{215}(0) ?

The general solution for y=cos^{215}(0)-sin^{215}(0) is y=1

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y=cos^{215}(0)-sin^{215}(0)

y = cos^{215} (0) - sin^{215} (0)

y = 1

Solution steps

y = cos^{215} (0) - sin^{215} (0)

Simplify

cos^{215} (0) - sin^{215} (0) : 1

cos^{215} (0) - sin^{215} (0)

cos^{215} (0) = 1

cos^{215} (0)

Simplify

cos (0) : 1

cos (0)

Use the following trivial identity:

cos (0) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 1^{215}

Apply rule

1^{a} = 1

= 1

sin^{215} (0) = 0

sin^{215} (0)

Simplify

sin (0) : 0

sin (0)

Use the following trivial identity:

sin (0) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0^{215}

Apply rule

0^{a} = 0

= 0

= 1 - 0

Simplify

y = 1

y = 1

sin (6 0^{\circ}) = (\frac{x}{81})

d = 7.2 sec (\cdot sin (3 0^{\circ} - 2 0^{\circ}))

\frac{a}{sin ( 4 4 ^{\circ} )} = \frac{9}{sin ( 6 6 ^{\circ} )}

c, sec (4 5^{\circ} + \frac{a}{2}) sec (4 5^{\circ} - \frac{a}{2}) = 2 sec (a)

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

What is the general solution for y=cos^{215}(0)-sin^{215}(0) ?
The general solution for y=cos^{215}(0)-sin^{215}(0) is y=1