Is cos^2(5θ)-sin^2(5θ)=cos(10θ) ?

The answer to whether cos^2(5θ)-sin^2(5θ)=cos(10θ) is True

Popular >

prove cos^2(5θ)-sin^2(5θ)=cos(10θ)

prove

cos^{2} (5 θ) - sin^{2} (5 θ) = cos (10 θ)

True

Solution steps

cos^{2} (5 θ) - sin^{2} (5 θ) = cos (10 θ)

Manipulating left side

cos^{2} (5 θ) - sin^{2} (5 θ)

Rewrite using trig identities

cos^{2} (5 θ) - sin^{2} (5 θ)

Use the Double Angle identity:

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

= cos (2 \cdot 5 θ)

Simplify

= cos (10 θ)

= cos (10 θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sin ( 2 x )}{sin ( x )} = \frac{2}{sec ( x )}

1 - tanh^{2} (z) = sech^{2} (z)

csc (s) = cot (s) sec (s)

csc^{4} (x) - cot^{4} (x) = 2 sec^{2} (x) - 1

Is cos^2(5θ)-sin^2(5θ)=cos(10θ) ?
The answer to whether cos^2(5θ)-sin^2(5θ)=cos(10θ) is True