Is 8cos^2(x)-8sin^2(x)=8-16sin^2(x) ?

The answer to whether 8cos^2(x)-8sin^2(x)=8-16sin^2(x) is True

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prove 8cos^2(x)-8sin^2(x)=8-16sin^2(x)

prove

8 cos^{2} (x) - 8 sin^{2} (x) = 8 - 16 sin^{2} (x)

True

Solution steps

8 cos^{2} (x) - 8 sin^{2} (x) = 8 - 16 sin^{2} (x)

Manipulating left side

8 cos^{2} (x) - 8 sin^{2} (x)

Rewrite using trig identities

8 cos^{2} (x) - 8 sin^{2} (x)

Use the Pythagorean identity:

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

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

= 8 (1 - sin^{2} (x)) - 8 sin^{2} (x)

Simplify

8 (1 - sin^{2} (x)) - 8 sin^{2} (x) : 8 - 16 sin^{2} (x)

8 (1 - sin^{2} (x)) - 8 sin^{2} (x)

Expand

8 (1 - sin^{2} (x)) : 8 - 8 sin^{2} (x)

8 (1 - sin^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = 8, b = 1, c = sin^{2} (x)

= 8 \cdot 1 - 8 sin^{2} (x)

Multiply the numbers:

8 \cdot 1 = 8

= 8 - 8 sin^{2} (x)

= 8 - 8 sin^{2} (x) - 8 sin^{2} (x)

Add similar elements:

- 8 sin^{2} (x) - 8 sin^{2} (x) = - 16 sin^{2} (x)

= 8 - 16 sin^{2} (x)

= 8 - 16 sin^{2} (x)

= 8 - 16 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (x) - sin (x) \cdot tan (x) = cos (x)

\frac{sec ( x ) csc ( x )}{cot ( x )} = sec^{2} (x)

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

cot (θ) sin (θ) sec (θ) = 1

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

Is 8cos^2(x)-8sin^2(x)=8-16sin^2(x) ?
The answer to whether 8cos^2(x)-8sin^2(x)=8-16sin^2(x) is True