Is sin^2(x)+4cos^2(x)=4-3sin^2(x) ?

The answer to whether sin^2(x)+4cos^2(x)=4-3sin^2(x) is True

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prove sin^2(x)+4cos^2(x)=4-3sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

sin^{2} (x) + 4 (1 - sin^{2} (x)) : - 3 sin^{2} (x) + 4

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

Expand

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

Multiply the numbers:

4 \cdot 1 = 4

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

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

Simplify

sin^{2} (x) + 4 - 4 sin^{2} (x) : - 3 sin^{2} (x) + 4

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

Group like terms

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

Add similar elements:

sin^{2} (x) - 4 sin^{2} (x) = - 3 sin^{2} (x)

= - 3 sin^{2} (x) + 4

= - 3 sin^{2} (x) + 4

= - 3 sin^{2} (x) + 4

= - 3 sin^{2} (x) + 4

= 4 - 3 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e sin (a + b) = sin (a) cos (b) + cos (a) sin (b)

p ro v e sin (B) + cos (B) cot (B) = csc (B)

p ro v e 3 sin (5 π - x) = 3 sin (x)

p ro v e cos^{2} (θ) = \frac{1 + cos ( 2 θ )}{2}

p ro v e \frac{cos ^{2} ( α )}{1 - sin ( α )} = 1 + sin (α)

Is sin^2(x)+4cos^2(x)=4-3sin^2(x) ?
The answer to whether sin^2(x)+4cos^2(x)=4-3sin^2(x) is True