Is 3sec^2(x)-2tan^2(x)-4=-2+sec^2(x) ?

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

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prove 3sec^2(x)-2tan^2(x)-4=-2+sec^2(x)

prove

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

True

Solution steps

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

Manipulating left side

3 sec^{2} (x) - 2 tan^{2} (x) - 4

Rewrite using trig identities

3 sec^{2} (x) - 2 tan^{2} (x) - 4

Use the Pythagorean identity:

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

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

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

Simplify

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

3 sec^{2} (x) - 2 (sec^{2} (x) - 1) - 4

Expand

- 2 (sec^{2} (x) - 1) : - 2 sec^{2} (x) + 2

- 2 (sec^{2} (x) - 1)

Apply the distributive law:

a (b - c) = ab - a c

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

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

Apply minus-plus rules

- (- a) = a

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

Multiply the numbers:

2 \cdot 1 = 2

= - 2 sec^{2} (x) + 2

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

Simplify

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

3 sec^{2} (x) - 2 sec^{2} (x) + 2 - 4

Add similar elements:

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

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

Add/Subtract the numbers:

2 - 4 = - 2

= sec^{2} (x) - 2

= sec^{2} (x) - 2

= sec^{2} (x) - 2

= sec^{2} (x) - 2

= - 2 + sec^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( 4 x )}{4} = \frac{sin ( x ) cos ( x )}{2}

18 = 32

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

sin (a + b) - sin (a - b) = 2 sin (a) sin (b)

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

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