Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

Question

Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

1 Answer

Impact of this question

7994 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-14T19:51:39

See below.

Explanation:

Using Identities:

${tan}^{2} x = \frac{{sin}^{2} x}{{cos}^{2} x}$ $color(red)(tan^2x=sin^2x/cos^2x)$

${sin}^{2} x + {cos}^{2} x = 1$ $color(red)(sin^2x+cos^2x=1)$
..................................................................................................................................

$L H S$ $LHS$

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

Multiply by ${cos}^{2} x$ $cos^2x$ :

$\frac{{cos}^{2} x - {sin}^{2} x}{{cos}^{2} x + {sin}^{2} x}$ $(cos^2x-sin^2x)/(cos^2x+sin^2x)$

${sin}^{2} x + {cos}^{2} x = 1$ $color(red)(sin^2x+cos^2x=1)$

${cos}^{2} x - {sin}^{2} x 88$ $cos^2x-sin^2xcolor(white)(88)$ ( ${cos}^{2} x = 1 - {sin}^{2} x$ $cos^2x= 1-sin^2x$ )

$1 - {sin}^{2} x - {sin}^{2} x$ $1-sin^2x-sin^2x$

$1 - 2 {sin}^{2} x$ $1-2sin^2x$

$L H S \equiv R H S$ $LHS -=RHS$

Science

Math

Humanities

... and beyond

Prove the identity (1-tan^2x)/(1+tan^2x) is same as 1-2sin^2x?

1 Answer

Explanation:

Related questions

Impact of this question