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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

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

(1 - cos (0)) (1 + sec (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

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

= (1 - 1) (1 + 1)

Simplify

= 0

The two sides are not equal

\Rightarrow False

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

cos^{2} (9 θ) - sin^{2} (9 θ) = cos (18 θ)

sec (x) csc (x) = 2 csc (2 x)

cos (u) + tan (u) sin (u) = sec (u)

sec (- θ) = sec (θ)

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