The answer to whether sin(t)cos(t)=1 is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sin(t)cos(t)=1

Solution

prove

sin (t) cos (t) = 1

False

Solution steps

sin (t) cos (t) = 1

Show that the two sides are not equal

For

sin (t) cos (t) = 1

plug in

t = 0

sin (0) cos (0) = 0

sin (0) cos (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

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

= 0 \cdot 1

Simplify

= 0

The two sides are not equal

\Rightarrow False

\frac{1}{1 - sin ( B )} = sec^{2} (B) + sec (B) tan (B)

tan (6 0^{\circ}) = \frac{2 tan ( 3 0 ^{\circ} )}{1 - tan ^{2} ( 3 0 ^{\circ} )}

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

cos (x) + sin (x) = 1

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