Is 1-2cos^2(4)=2sin^2(4)-1 ?

The answer to whether 1-2cos^2(4)=2sin^2(4)-1 is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove 1-2cos^2(4)=2sin^2(4)-1

prove

1 - 2 cos^{2} (4) = 2 sin^{2} (4) - 1

True

Solution steps

1 - 2 cos^{2} (4) = 2 sin^{2} (4) - 1

Manipulating left side

1 - 2 cos^{2} (4)

Rewrite using trig identities

1 - 2 cos^{2} (4)

Use the Pythagorean identity:

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

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

= 1 - 2 (1 - sin^{2} (4))

1 - 2 (1 - sin^{2} (4)) = 2 sin^{2} (4) - 1

1 - 2 (1 - sin^{2} (4))

Expand

- 2 (1 - sin^{2} (4)) : - 2 + 2 sin^{2} (4)

- 2 (1 - sin^{2} (4))

Apply the distributive law:

a (b - c) = ab - a c

a = - 2, b = 1, c = sin^{2} (4)

= - 2 \cdot 1 - (- 2) sin^{2} (4)

Apply minus-plus rules

- (- a) = a

= - 2 \cdot 1 + 2 sin^{2} (4)

Multiply the numbers:

2 \cdot 1 = 2

= - 2 + 2 sin^{2} (4)

= 1 - 2 + 2 sin^{2} (4)

Subtract the numbers:

1 - 2 = - 1

= 2 sin^{2} (4) - 1

= 2 sin^{2} (4) - 1

= 2 sin^{2} (4) - 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( θ )}{cot ( θ ) + tan ( θ )} = sin^{2} (θ)

2 sin (x) + (2 + 2) = - 2 csc (x)

sin (8 a) = 4 sin (2 a) cos (2 a) cos (4 a)

sin^{2} (2 x) = \frac{1}{2 ( 1 - cos ^{4} ( x ) )}

\frac{( 1 - sin ( a ) )}{cos ( a )} = cos (a)

Is 1-2cos^2(4)=2sin^2(4)-1 ?
The answer to whether 1-2cos^2(4)=2sin^2(4)-1 is True