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

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

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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

p ro v e sin (8 a) = 4 sin (2 a) cos (2 a) cos (4 a)

p ro v e csc^{2} (x) (tan (x)) - (tan (x)) = cot (x)

p ro v e \frac{sin ( 3 a )}{sin ( a )} = 2 cos (2 a) + 1

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

p ro v e \frac{cot ^{2} ( x ) + 1}{cot ^{2} ( x ) - 1} = sec (2 x)

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