Is 2cos^2(u)-cos(2u)=1 ?

The answer to whether 2cos^2(u)-cos(2u)=1 is True

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prove 2cos^2(u)-cos(2u)=1

prove

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

True

Solution steps

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

Manipulating left side

2 cos^{2} (u) - cos (2 u)

Rewrite using trig identities

2 cos^{2} (u) - cos (2 u)

Use the Double Angle identity:

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

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

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

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

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

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

Distribute parentheses

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

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 2 cos^{2} (u) + 1

= 2 cos^{2} (u) - 2 cos^{2} (u) + 1

Add similar elements:

2 cos^{2} (u) - 2 cos^{2} (u) = 0

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

sec^{4} (θ) = sec^{2} (θ) tan^{2} (θ) + sec^{2} (θ)

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

tan (θ) sec (θ) csc (θ) = 1 + tan^{2} (θ)

\frac{cos ( t )}{1 - sin ( t )} - tan (t) = sec (t)

\frac{1 - cos ( x )}{\frac{1}{c o s ( x )} - 1} = cos (x)