Is 9cos^2(x)-9sin^2(x)=9-18sin^2(x) ?

The answer to whether 9cos^2(x)-9sin^2(x)=9-18sin^2(x) is True

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prove 9cos^2(x)-9sin^2(x)=9-18sin^2(x)

prove

9 cos^{2} (x) - 9 sin^{2} (x) = 9 - 18 sin^{2} (x)

True

Solution steps

9 cos^{2} (x) - 9 sin^{2} (x) = 9 - 18 sin^{2} (x)

Manipulating left side

9 cos^{2} (x) - 9 sin^{2} (x)

Rewrite using trig identities

9 cos^{2} (x) - 9 sin^{2} (x)

Use the Pythagorean identity:

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

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

= 9 (1 - sin^{2} (x)) - 9 sin^{2} (x)

Simplify

9 (1 - sin^{2} (x)) - 9 sin^{2} (x) : 9 - 18 sin^{2} (x)

9 (1 - sin^{2} (x)) - 9 sin^{2} (x)

Expand

9 (1 - sin^{2} (x)) : 9 - 9 sin^{2} (x)

9 (1 - sin^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = 9, b = 1, c = sin^{2} (x)

= 9 \cdot 1 - 9 sin^{2} (x)

Multiply the numbers:

9 \cdot 1 = 9

= 9 - 9 sin^{2} (x)

= 9 - 9 sin^{2} (x) - 9 sin^{2} (x)

Add similar elements:

- 9 sin^{2} (x) - 9 sin^{2} (x) = - 18 sin^{2} (x)

= 9 - 18 sin^{2} (x)

= 9 - 18 sin^{2} (x)

= 9 - 18 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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Is 9cos^2(x)-9sin^2(x)=9-18sin^2(x) ?
The answer to whether 9cos^2(x)-9sin^2(x)=9-18sin^2(x) is True