Is 2sec^2(x)=(1+2tan(x))^2 ?

The answer to whether 2sec^2(x)=(1+2tan(x))^2 is False

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prove 2sec^2(x)=(1+2tan(x))^2

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

2 sec^{2} (0) = 2

2 sec^{2} (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 1

= 2 \cdot 1^{2}

Simplify

= 2

(1 + 2 tan (0))^{2} = 1

(1 + 2 tan (0))^{2}

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= (1 + 2 \cdot 0)^{2}

Simplify

= 1

The two sides are not equal

\Rightarrow False

sin^{6} (a) + cos^{6} (a) = 1 - 3 sin^{2} (a) \cdot cos^{2} (a)

sin (- 3 x) = - sin (3 x)

2 tan (θ) = sin (θ)

cos (x) + sin (x) = tan (x) + 1

csc (2 θ) = \frac{( csc ( θ ) sec ( θ ) )}{2}

Is 2sec^2(x)=(1+2tan(x))^2 ?
The answer to whether 2sec^2(x)=(1+2tan(x))^2 is False