Is 5sin^2(x)+5cos^2(x)=5 ?

The answer to whether 5sin^2(x)+5cos^2(x)=5 is True

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prove 5sin^2(x)+5cos^2(x)=5

prove

5 sin^{2} (x) + 5 cos^{2} (x) = 5

True

Solution steps

5 sin^{2} (x) + 5 cos^{2} (x) = 5

Manipulating left side

5 sin^{2} (x) + 5 cos^{2} (x)

Factor

5 cos^{2} (x) + 5 sin^{2} (x) : 5 (cos^{2} (x) + sin^{2} (x))

5 cos^{2} (x) + 5 sin^{2} (x)

Factor out common term

5

= 5 (cos^{2} (x) + sin^{2} (x))

= (cos^{2} (x) + sin^{2} (x)) \cdot 5

Rewrite using trig identities

(cos^{2} (x) + sin^{2} (x)) \cdot 5

Use the Pythagorean identity:

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

= 1 \cdot 5

Simplify

= 5

= 5

We showed that the two sides could take the same form

\Rightarrow True