The answer to whether sin(x)+5=4 is False

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prove sin(x)+5=4

Solution

prove

sin (x) + 5 = 4

False

Solution steps

sin (x) + 5 = 4

Show that the two sides are not equal

For

sin (x) + 5 = 4

plug in

x = 0

sin (0) + 5 = 5

sin (0) + 5

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

= 0 + 5

Simplify

= 5

The two sides are not equal

\Rightarrow False

\frac{1}{csc ( x )} = \frac{sin ( x )}{1}

sin^{2} (x) - 1 = 2 tan (x) - 1

2 - csc^{2} (θ) = 1 + cot^{2} (θ)

sin (\frac{π}{6} + b) + cos (\frac{π}{3} + b) = cos (b)

cos^{2} (x) - sin^{2} (x)