Is 4cos^2(x)+4sin^2(x)=4 ?

The answer to whether 4cos^2(x)+4sin^2(x)=4 is True

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prove 4cos^2(x)+4sin^2(x)=4

prove

4 cos^{2} (x) + 4 sin^{2} (x) = 4

True

Solution steps

4 cos^{2} (x) + 4 sin^{2} (x) = 4

Manipulating left side

4 cos^{2} (x) + 4 sin^{2} (x)

Rewrite using trig identities

4 cos^{2} (x) + 4 sin^{2} (x)

Use the Pythagorean identity:

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

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

= 4 cos^{2} (x) + 4 (1 - cos^{2} (x))

4 cos^{2} (x) + 4 (1 - cos^{2} (x)) = 4

4 cos^{2} (x) + 4 (1 - cos^{2} (x))

Expand

4 (1 - cos^{2} (x)) : 4 - 4 cos^{2} (x)

4 (1 - cos^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = 4, b = 1, c = cos^{2} (x)

= 4 \cdot 1 - 4 cos^{2} (x)

Multiply the numbers:

4 \cdot 1 = 4

= 4 - 4 cos^{2} (x)

= 4 cos^{2} (x) + 4 - 4 cos^{2} (x)

Simplify

4 cos^{2} (x) + 4 - 4 cos^{2} (x) : 4

4 cos^{2} (x) + 4 - 4 cos^{2} (x)

Group like terms

= 4 cos^{2} (x) - 4 cos^{2} (x) + 4

Add similar elements:

4 cos^{2} (x) - 4 cos^{2} (x) = 0

= 4

= 4

= 4

= 4

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) + cot (θ) = (sec (θ)) (csc (θ))

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

\frac{csc ( t ) + 1}{cot ( t )} = \frac{cot ( t )}{csc ( t ) - 1}

(3 sin (θ) - 3 cos (θ))^{2} = 9 - 9 sin (2 θ)

\frac{cos ( x )}{sin ^{2} ( x )} = csc (x) cot (x)