prove 1=sec^2(x)

Solution

prove

1 = sec^{2} (x)

False

Solution steps

1 = sec^{2} (x)

Show that the two sides are not equal

For

1 = sec^{2} (x)

plug in

x = 1

sec^{2} (1) = 3.42551 \dots

sec^{2} (1)

Refine to a decimal form

= 3.42551 \dots

The two sides are not equal

\Rightarrow False

\frac{csc ( x )}{csc ( x ) - sin ( x )} = sec^{2} (x)

(sin^{2} (x)) - cos^{2} (x) = 2 sin^{2} (x) - 1

csc^{2} (t) tan^{2} (t) - 1 = tan^{2} (t)

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

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