Is sin(45)cot(45)=cos(45) ?

The answer to whether sin(45)cot(45)=cos(45) is True

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prove sin(45)cot(45)=cos(45)

prove

sin (4 5^{\circ}) cot (4 5^{\circ}) = cos (4 5^{\circ})

True

Solution steps

sin (4 5^{\circ}) cot (4 5^{\circ}) = cos (4 5^{\circ})

Manipulating left side

sin (4 5^{\circ}) cot (4 5^{\circ})

Simplify

cot (4 5^{\circ}) sin (4 5^{\circ}) : \frac{2}{2}

cot (4 5^{\circ}) sin (4 5^{\circ})

Simplify

cot (4 5^{\circ}) : 1

cot (4 5^{\circ})

Use the following trivial identity:

cot (4 5^{\circ}) = 1

cot (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

= 1 \cdot sin (4 5^{\circ})

Simplify

sin (4 5^{\circ}) : \frac{2}{2}

sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= 1 \cdot \frac{2}{2}

Multiply:

1 \cdot \frac{2}{2} = \frac{2}{2}

= \frac{2}{2}

= \frac{2}{2}

Manipulating right side

cos (4 5^{\circ})

Simplify

= \frac{2}{2}

We showed that the two sides could take the same form

\Rightarrow True

p ro v e csc (θ) - sin (θ) = cot (θ) csc (θ)

p ro v e cos (8 θ) = cos^{2} (4 θ) - sin^{2} (4 θ)

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

p ro v e tan^{2} (θ) = sec (θ) csc (θ) tan (θ) - 1

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

Is sin(45)cot(45)=cos(45) ?
The answer to whether sin(45)cot(45)=cos(45) is True