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))

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

Rewrite using trig identities

= 2

We showed that the two sides could take the same form

\Rightarrow True

\frac{3}{8} = \frac{1}{4} sin (\frac{2 π}{3})

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

tan (\frac{π}{4} - x) = \frac{1 - tan ( x )}{1 + tan ( x )}

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

cos (3 x) = \frac{2}{2}