Question

Show that: 1 + tan2(x) = sec2(x) ​

Answer 1

$\large{\underline{\underline{\bf{\red{AnsWer - :}}}}}$ ➜

$tan(x) \: = \: \frac{sin(x)}{cos(x)}$

        $and$

$sec(x) \: = \: \frac{1}{cos(x)}$

      $so \: you \: get \:$

$1\: + \: \frac{sin^{2}(x) }{cos^{2}(x)}$

        $rearranging$

$\frac{cos^{2}(x)\: + \: sin^{2}(x) }{(cos^{2}(x)) } \: = \frac{1}{(cos^{2}(x)) }$

     $cancel \: denominators$

$so\: that : \:cos^{2} (x) \:+ \: sin^{2} (x) \: = \: 1 \: which \: is \: true$

Answer 2

$\huge\bold\color{blue}{answer:-}$

cos^2(x)+sin^2(x)=1

Divide both sides by cos2(x) to get:

cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)=1/cos2(x)

which simplifies to:

1+tan2(x)=sec2(x)