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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

cos (0) tan (0) sec (- 0) = 0

cos (0) tan (0) sec (- 0)

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}

= cos (0) \cdot 0 \cdot sec (- 0)

= cos (0) \cdot 0 \cdot sec (- 0)

Simplify

= 0

sin (0) - 1 = - 1

sin (0) - 1

Use the following trivial identity:

sin (0) = 0

sin (0)

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

= 0

= 0 - 1

Simplify

= - 1

The two sides are not equal

\Rightarrow False

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

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

cos (x - y) - cos (x + y) = 2 sin (x) sin (y)

tan (θ) csc (θ) = sec (θ)

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

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