Is csc(θ)= 1/(sec(θ)) ?

The answer to whether csc(θ)= 1/(sec(θ)) is False

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prove csc(θ)= 1/(sec(θ))

prove

csc (θ) = \frac{1}{sec ( θ )}

False

Solution steps

csc (θ) = \frac{1}{sec ( θ )}

Show that the two sides are not equal

For

csc (θ) = \frac{1}{sec ( θ )}

plug in

θ = 1

csc (1) = 1.18839 \dots

csc (1)

Refine to a decimal form

= 1.18839 \dots

\frac{1}{sec ( 1 )} = 0.54030 \dots

\frac{1}{sec ( 1 )}

Refine to a decimal form

= 0.54030 \dots

The two sides are not equal

\Rightarrow False

cot (2 x) + tan (x) = csc (2 x)

2 cos^{2} (\frac{x}{2}) - 1 = cos (x)

\frac{csc ( z )}{sec ( z )} = cot (z)

\frac{tan ( θ ) cot ( θ )}{sec ( θ )} = cos (θ)

\frac{sin ( x ) + sin ( 3 x )}{cos ( x ) - cos ( 3 x )} = cot (x)