Question

the value of 1-tan2 15/1+tan2 15​

Answer 1

Answer:

★Question★

$\bf \:Evaluate : \dfrac{1 - {tan}^{2}15 °}{1 + {tan}^{2} 15°}$

★Answer★

★Identity used :-

$\bf \:cos2x = \dfrac{1 - {tan}^{2}x }{1 + {tan}^{2} x}$

★Solution:

$\bf \:\dfrac{1 - {tan}^{2}15° }{1 + {tan}^{2} 15°}$

$\bf\implies \:cos2(15°)$

$\bf\implies \:cos30°$

$\bf\implies \:\dfrac{ \sqrt{3} }{2}$

____________________________________________

★Additional Information★

★Important Formula's

$\bf \:★sin2x = 2sinx \: cosx = \dfrac{2tanx}{1 + {tan}^{2} x}$

$\bf \:★cos2x = 1 - 2 {sin}^{2} x =2 {cos}^{2} x - 1 = {cos}^{2} x - {sin}^{2} x$

$\bf \:★tan2x = \dfrac{2tanx}{1 - {tan}^{2}x }$

$\bf \:★sin3x = 3sinx - {4sin}^{3} x$

$\bf \:★cos3x = {4cos}^{3} x - 3cosx$

_____________________________________________