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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

= sin^{2} (x) - 3 (1 - sin^{2} (x))

Simplify

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

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

Expand

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

Apply minus-plus rules

- (- a) = a

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

Multiply the numbers:

3 \cdot 1 = 3

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

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

Simplify

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

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

Group like terms

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

Add similar elements:

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

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) + 6 = sec^{2} (x) + 5

tan (\frac{π}{2} - θ) tan (θ) = 1

(1 - sin^{2} (x)) csc^{2} (x) = cot^{2} (x)

\frac{1}{2 tan ( x ) ( 1 - sin ^{2} ( x ) )} = csc (2 x)

sin (t) tan (t) = \frac{1 - cos ^{2} ( t )}{cos ( t )}

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