Is (sec(x)+tan(x))(1-sec(x))=cos(x) ?

The answer to whether (sec(x)+tan(x))(1-sec(x))=cos(x) is False

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prove (sec(x)+tan(x))(1-sec(x))=cos(x)

prove

(sec (x) + tan (x)) (1 - sec (x)) = cos (x)

False

Solution steps

(sec (x) + tan (x)) (1 - sec (x)) = cos (x)

Show that the two sides are not equal

For

(sec (x) + tan (x)) (1 - sec (x)) = cos (x)

plug in

x = 0

(sec (0) + tan (0)) (1 - sec (0)) = 0

(sec (0) + tan (0)) (1 - sec (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

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 + 0) (1 - 1)

Simplify

= 0

cos (0) = 1

cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 1

The two sides are not equal

\Rightarrow False

tan (x) cos (2 x) = sin (2 x) - tan (x)

\frac{sin ^{2} ( θ )}{tan ^{2} ( θ )} = cos^{2} (θ)

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

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

\frac{1}{csc ( x )} + 1 = sin (x) + 1

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