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

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

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

prove

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

True

Solution steps

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

Manipulating left side

- (sin (x) + 2) (sin (x) - 2)

Expand

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

- (- 2 + sin (x)) (2 + sin (x))

Expand

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

(- 2 + sin (x)) (2 + sin (x))

Apply Difference of Two Squares Formula:

(a - b) (a + b) = a^{2} - b^{2}

a = sin (x), b = 2

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

2^{2} = 4

= sin^{2} (x) - 4

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

Distribute parentheses

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

Apply minus-plus rules

- (- a) = a, - (a) = - a

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

= 4 - sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{cot ^{2} ( x ) sin ^{2} ( x )} = 1 + tan^{2} (x)

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

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

csc^{2} (θ) sec^{2} (θ) - csc^{2} (θ) = sec^{2} (θ)

\frac{cos ( x )}{1 + sin ( x )} = - tan (x) + sec (x)

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