Question

Show that Tan^2 theeta - 1/cos^2theeta=-1

Answer 1

Answer:

See attached picture.

Answer 2

$\boxed{ \huge \mathfrak \red{{solution}}}$

Given,

$\mathfrak{to \: prove} \\ { \tan }^{2} \alpha - \frac{1}{ \cos^{2} \alpha } = - 1$

LHS

${ \tan }^{2} \alpha - \sec^{2} \alpha$

As we know that,

sec^2@-tan^2@=1

take minus common

$\rightarrow - (tan ^{2} \alpha - \sec^{2} \alpha ) = 1$

$\rightarrow \tan^{2} \alpha - { \sec }^{2} \alpha = - 1$

OR

$\rightarrow \: tan^{2} \alpha - \frac{1}{ \cos{}^{2} \alpha } = - 1$

$\boxed{proved}$