Is 2cos^2(x)+sin^2(x)=1+cos^2(x) ?

The answer to whether 2cos^2(x)+sin^2(x)=1+cos^2(x) is True

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prove 2cos^2(x)+sin^2(x)=1+cos^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Group like terms

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

Add similar elements:

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

= cos^{2} (x) + 1

= cos^{2} (x) + 1

= cos^{2} (x) + 1

= 1 + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (B) - sin (B) = cot (B) cos (B)

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

cos (2 a + a) = - 3 cos (a) + 4 cos^{3} (a)

cot (2 θ) = \frac{1}{2} sec (θ) csc (θ) - tan (θ)

csc^{2} (θ) - cos (θ) sec (θ) = cot^{2} (θ)

Is 2cos^2(x)+sin^2(x)=1+cos^2(x) ?
The answer to whether 2cos^2(x)+sin^2(x)=1+cos^2(x) is True