Is prove-2sin(2(x+45))=2cos(2x) ?

The answer to whether prove-2sin(2(x+45))=2cos(2x) is False

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove-2sin(2(x+45))=2cos(2x)

prove

- 2 sin (2 (x + 45)) = 2 cos (2 x)

False

Solution steps

- 2 sin (2 (x + 45)) = 2 cos (2 x)

Show that the two sides are not equal

For

- 2 sin (2 (x + 45)) = 2 cos (2 x)

plug in

x = 0

- 2 sin (2 (0 + 45)) = - 1.78799 \dots

- 2 sin (2 (0 + 45))

Refine to a decimal form

= - 1.78799 \dots

2 cos (2 \cdot 0) = 2

2 cos (2 \cdot 0)

Simplify

= 2 cos (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

= 2 \cdot 1

Simplify

= 2

The two sides are not equal

\Rightarrow False

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

(sin (\frac{4 π}{3})) = - \frac{3}{2}

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

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

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

Is prove-2sin(2(x+45))=2cos(2x) ?
The answer to whether prove-2sin(2(x+45))=2cos(2x) is False