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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Factor

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

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

Factor out common term

2

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

= (cos^{2} (x) + sin^{2} (x)) \cdot 2

Rewrite using trig identities

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

Use the Pythagorean identity:

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

= 1 \cdot 2

Simplify

= 2

= 2

We showed that the two sides could take the same form

\Rightarrow True