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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= 3 (1 - cos^{2} (x)) + 4 cos^{2} (x)

Simplify

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

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

Expand

3 (1 - cos^{2} (x)) : 3 - 3 cos^{2} (x)

3 (1 - cos^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = 3, b = 1, c = cos^{2} (x)

= 3 \cdot 1 - 3 cos^{2} (x)

Multiply the numbers:

3 \cdot 1 = 3

= 3 - 3 cos^{2} (x)

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

Add similar elements:

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

= 3 + cos^{2} (x)

= 3 + cos^{2} (x)

= 3 + cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e tan (\frac{π}{2} - θ) tan (θ) = 1

p ro v e (1 - sin^{2} (x)) csc^{2} (x) = cot^{2} (x)

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

p ro v e \frac{csc ( x )}{sin ( x )} - \frac{cot ( x )}{tan ( x )} = 1

p ro v e \frac{csc ( x ) - cot ( x )}{sec ( x ) - 1} = cot (x)

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