Question

If tan a + 1 by tana equals 2 find tan square a + 1 by tan square a

Answer 1

Answer:

GIVEN THAT:

$\tan(a) + \frac{1}{ \tan(a) } = 2$

TO FIND:

Value of

$\tan {}^{2} (a) + \frac{1}{ \tan {}^{2} ( a) }$

$\green{ANSWER}$

Squaring both sides

$( \tan(a) + \frac{1}{ \tan( a) } ) {}^{2} = (2) {}^{2}$

$\tan {}^{2} ( a ) + \frac{1}{ \tan {}^{2} (a) } + 2 \tan(a) \times \frac{1}{ \tan(a) } = 4$

$\tan {}^{2} (a) + \frac{1}{ \tan {}^{2} (a) } = - 2 + 4$

$\tan {}^{2} (a) + \frac{1}{ \tan {}^{2} ( a ) } = 2$