Is tan(4Θ)+tan(2Θ)=sec(4Θ)-sec(2Θ) ?

The answer to whether tan(4Θ)+tan(2Θ)=sec(4Θ)-sec(2Θ) is False

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prove tan(4Θ)+tan(2Θ)=sec(4Θ)-sec(2Θ)

prove

tan (4Θ) + tan (2Θ) = sec (4Θ) - sec (2Θ)

False

Solution steps

tan (4Θ) + tan (2Θ) = sec (4Θ) - sec (2Θ)

Show that the two sides are not equal

For

tan (4Θ) + tan (2Θ) = sec (4Θ) - sec (2Θ)

plug in

Θ = 1

tan (4 \cdot 1) + tan (2 \cdot 1) = - 1.02721 \dots

tan (4 \cdot 1) + tan (2 \cdot 1)

Refine to a decimal form

= - 1.02721 \dots

sec (4 \cdot 1) - sec (2 \cdot 1) = 0.87311 \dots

sec (4 \cdot 1) - sec (2 \cdot 1)

Refine to a decimal form

= 0.87311 \dots

The two sides are not equal

\Rightarrow False

tan (\frac{3 π}{2} - x) = - tan (x)

cos (2 α) = cos (α + α)

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

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

- 3 (0) cos (3 t) + 3 (1) sin (3 t) = 3 sin (3 t)

Is tan(4Θ)+tan(2Θ)=sec(4Θ)-sec(2Θ) ?
The answer to whether tan(4Θ)+tan(2Θ)=sec(4Θ)-sec(2Θ) is False