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

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

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

prove

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

True

Solution steps

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

Manipulating left side

3 + sin^{2} (x)

Rewrite using trig identities

3 + sin^{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)

Simplify

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

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

= 4 - cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{4} (m) - cos^{4} (m) = 1 - 2 cos^{2} (m)

\frac{\frac{1}{c o s ( x )} - 1}{1 - cos ( x )} = sec (x)

tan (13 5^{\circ} + a) = \frac{tan ( a ) - 1}{tan ( a ) + 1}

tan (\frac{x}{2}) = \frac{tan ( x )}{( sec ( x ) + 1 )}

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