Is 7-sin(x)=1-(cos^2(x))/(1-sin(x)) ?

The answer to whether 7-sin(x)=1-(cos^2(x))/(1-sin(x)) is False

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prove 7-sin(x)=1-(cos^2(x))/(1-sin(x))

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

7 - sin (0) = 7

7 - sin (0)

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

= 7 - 0

Simplify

= 7

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

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

Simplify

= 0

The two sides are not equal

\Rightarrow False

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

sin^{4} (x) = (sin^{2} (x))^{2}

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

\frac{cot ( α )}{cos ( α )} = csc (α)

cos^{(2)} (θ) (1 + tan^{(2)} (θ)) = 1

Is 7-sin(x)=1-(cos^2(x))/(1-sin(x)) ?
The answer to whether 7-sin(x)=1-(cos^2(x))/(1-sin(x)) is False