Is cos(0)tan(0)=sin(0) ?

The answer to whether cos(0)tan(0)=sin(0) is True

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prove cos(0)tan(0)=sin(0)

prove

cos (0) tan (0) = sin (0)

True

Solution steps

cos (0) tan (0) = sin (0)

Manipulating left side

cos (0) tan (0)

Simplify

cos (0) tan (0) : 0

cos (0) tan (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 \cdot tan (0)

Simplify

tan (0) : 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= 1 \cdot 0

Apply rule

0 \cdot a = 0

= 0

= 0

Manipulating right side

sin (0)

Simplify

= 0

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{π}{6}) = \frac{4}{3} cos^{3} (\frac{π}{6})

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

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

tan (- \frac{π}{4}) = - 1

(cos (θ) - sin (θ))^{2} = 1 - sin (2 θ)