Is cos^2(x)-2sin^2(x)=3cos^2(x)-2 ?

The answer to whether cos^2(x)-2sin^2(x)=3cos^2(x)-2 is True

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prove cos^2(x)-2sin^2(x)=3cos^2(x)-2

prove

cos^{2} (x) - 2 sin^{2} (x) = 3 cos^{2} (x) - 2

True

Solution steps

cos^{2} (x) - 2 sin^{2} (x) = 3 cos^{2} (x) - 2

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

cos^{2} (x) - 2 (1 - cos^{2} (x)) : 3 cos^{2} (x) - 2

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

Expand

- 2 (1 - cos^{2} (x)) : - 2 + 2 cos^{2} (x)

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

Apply the distributive law:

a (b - c) = ab - a c

a = - 2, b = 1, c = cos^{2} (x)

= - 2 \cdot 1 - (- 2) cos^{2} (x)

Apply minus-plus rules

- (- a) = a

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

Multiply the numbers:

2 \cdot 1 = 2

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

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

Simplify

cos^{2} (x) - 2 + 2 cos^{2} (x) : 3 cos^{2} (x) - 2

cos^{2} (x) - 2 + 2 cos^{2} (x)

Group like terms

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

Add similar elements:

cos^{2} (x) + 2 cos^{2} (x) = 3 cos^{2} (x)

= 3 cos^{2} (x) - 2

= 3 cos^{2} (x) - 2

= 3 cos^{2} (x) - 2

= 3 cos^{2} (x) - 2

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + cos ( 2 x )}{sec ^{2} ( x )} = 2 cos^{4} (x)

sin (x) sec (x) cot (x) = cot (x)

sin (\frac{7 π}{4}) = sin (\frac{- π}{4})

cos (π - θ) = cos (θ)

tan (x) = \frac{4}{5}

Is cos^2(x)-2sin^2(x)=3cos^2(x)-2 ?
The answer to whether cos^2(x)-2sin^2(x)=3cos^2(x)-2 is True