Is tan(x)(cos(x))/(1+sin(x))=sec(x) ?

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

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prove tan(x)(cos(x))/(1+sin(x))=sec(x)

prove

tan (x) \frac{cos ( x )}{1 + sin ( x )} = sec (x)

False

Solution steps

tan (x) \frac{cos ( x )}{1 + sin ( x )} = sec (x)

Show that the two sides are not equal

For

tan (x) \frac{cos ( x )}{1 + sin ( x )} = sec (x)

plug in

x = 0

tan (0) \frac{cos ( 0 )}{1 + sin ( 0 )} = 0

tan (0) \frac{cos ( 0 )}{1 + sin ( 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}

= 0 \cdot \frac{cos ( 0 )}{1 + sin ( 0 )}

= 0 \cdot \frac{cos ( 0 )}{1 + sin ( 0 )}

Simplify

= 0

sec (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

= 1

The two sides are not equal

\Rightarrow False

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

cos (x - 9 0^{\circ}) = sin (x)

\frac{1 + sec ( B )}{tan ( B ) + sin ( B )} = csc (B)

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

\frac{sec ( v ) - cos ( v )}{sec ( v )} = sin^{2} (v)

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