Is cos^2(9θ)-sin^2(9θ)=cos(18θ) ?

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

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prove cos^2(9θ)-sin^2(9θ)=cos(18θ)

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (9 θ) - sin^{2} (9 θ)

Rewrite using trig identities

cos^{2} (9 θ) - sin^{2} (9 θ)

Use the Double Angle identity:

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

= cos (2 \cdot 9 θ)

Simplify

= cos (18 θ)

= cos (18 θ)

We showed that the two sides could take the same form

\Rightarrow True

sec (x) csc (x) = 2 csc (2 x)

cos (u) + tan (u) sin (u) = sec (u)

sec (- θ) = sec (θ)

sin (\frac{11 π}{12}) = sin (\frac{3 π}{4} + \frac{π}{6})

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

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