Question

If sec theta=14x+x ,then prove that sec theta+tan theta =2x or 12x.

Answer 1

$let \: sec \: a \: + tan \: a \: = \: n$
$sec { }^{2} \:a \: - tan {}^{2} a = 1$
${sec \: a \: - \: tan \: a \: } \times sec \: a \: + tan \: a \: = \: 1$
$sec \: a \: - tan \: a \: = \: 1 \div n$
By elemination first and fourth equation,
$2sec \: a \: = \: n \: + \: 1 \div n$
$2 \times 14 x \: + \:1 \div x \: = \: n \: + \: 1 \div n$
$n \: = \: 28x \: or \: 2 \: \div x$