Is 4sec^2(θ)-3=1+4tan^2(θ) ?

The answer to whether 4sec^2(θ)-3=1+4tan^2(θ) is True

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prove 4sec^2(θ)-3=1+4tan^2(θ)

prove

4 sec^{2} (θ) - 3 = 1 + 4 tan^{2} (θ)

True

Solution steps

4 sec^{2} (θ) - 3 = 1 + 4 tan^{2} (θ)

Manipulating left side

4 sec^{2} (θ) - 3

Rewrite using trig identities

4 sec^{2} (θ) - 3

Use the Pythagorean identity:

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

= 4 (tan^{2} (θ) + 1) - 3

Simplify

4 (tan^{2} (θ) + 1) - 3 : 4 tan^{2} (θ) + 1

4 (tan^{2} (θ) + 1) - 3

Expand

4 (tan^{2} (θ) + 1) : 4 tan^{2} (θ) + 4

4 (tan^{2} (θ) + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = 4, b = tan^{2} (θ), c = 1

= 4 tan^{2} (θ) + 4 \cdot 1

Multiply the numbers:

4 \cdot 1 = 4

= 4 tan^{2} (θ) + 4

= 4 tan^{2} (θ) + 4 - 3

Add/Subtract the numbers:

4 - 3 = 1

= 4 tan^{2} (θ) + 1

= 4 tan^{2} (θ) + 1

= 4 tan^{2} (θ) + 1

= 1 + 4 tan^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

Is 4sec^2(θ)-3=1+4tan^2(θ) ?
The answer to whether 4sec^2(θ)-3=1+4tan^2(θ) is True