# Prove that  1200secx(2(sec^2x)-1) -= 1220 ((1+sin^2x)/cos^2x) ?

Feb 4, 2018

The given statement is not an identity.

#### Explanation:

We seek to prove that:

$1200 \sec x \left(2 \left({\sec}^{2} x\right) - 1\right) \equiv 1220 \left(\frac{1 + {\sin}^{2} x}{\cos} ^ 2 x\right)$

We can disprove this identity using a Counter Example:

Consider the case $x = 0$, then:

$L H S = 1200 \sec 0 \left(2 \left({\sec}^{2} 0\right) - 1\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 1200 \left(2 - 1\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 1200$

And:

$R H S = 1220 \left(\frac{1 + {\sin}^{2} 0}{\cos} ^ 2 0\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 1220 \left(\frac{1 + 0}{1}\right)$
$\setminus \setminus \setminus \setminus \setminus \setminus \setminus \setminus = 1220$

And $L H S \ne R H S$ so the given statement is not an identity.