Is 1-(cos^2(x))/(1+sin^2(x))=sin(s) ?

The answer to whether 1-(cos^2(x))/(1+sin^2(x))=sin(s) is False

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prove 1-(cos^2(x))/(1+sin^2(x))=sin(s)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

For

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

plug in

s = 1

1 - \frac{cos ^{2} ( 0 )}{1 + sin ^{2} ( 0 )} = 0

1 - \frac{cos ^{2} ( 0 )}{1 + sin ^{2} ( 0 )}

Use the following trivial identity:

cos (0) = 1

cos (0)

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

Use the following trivial identity:

sin (0) = 0

sin (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

= 1 - \frac{1 ^{2}}{1 + 0 ^{2}}

Simplify

= 0

sin (1) = 0.84147 \dots

sin (1)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False

p ro v e csc (x) = \frac{1}{sin ( x )} = 2

p ro v e 5 - 5 + 5 - 5 - 5 - 5 + 5 - 5 + 5 + 5 - 5 = - 5

p ro v e 1 + cos^{4} (x) - sin^{4} (x) = 2 cos^{2} (x)

p ro v e cot (x) - sec (x) csc (x) cos (2 x) = tan (x)

p ro v e \frac{1}{tan ( x )} + \frac{1}{cot ( x )} = sec (x) csc (x)

Is 1-(cos^2(x))/(1+sin^2(x))=sin(s) ?
The answer to whether 1-(cos^2(x))/(1+sin^2(x))=sin(s) is False