Question

sin a +cos a /sin a - cos a=3 then sin a^4-cos a^4=?​

Answer 1

${ \green{ \underline{ \underline{ \huge{ \mathfrak \red{answer}}}}}}$

$\frac{ \sin \: a \: + \cos \: a }{ \sin \: a - \cos \: a } = 3$

$\frac{( \sin \: a \: + \cos \: a) + ( \sin \: a - \cos \: a }{( \sin \: a + \cos \: a) - ( \sin \: a \: - \cos \: a) }$

$\frac{3 + 1}{3 - 1}$

$\frac{2 \sin \: a }{2 \cos \: a }$

$\frac{4}{2}$

$\tan \: a = 2$

$= { \tan }^{2}a = { \tan}^{2} a = 4 = 1 + { \tan }^{2} a = 5$

$\sin \: a \: = \sqrt{1 - \frac{1}{5} }$

$= \frac{2}{ \sqrt{5} }$

${ \sin }^{4} a - { \cos }^{3} a$

$( { \frac{2}{ \sqrt{5} } }^{4} ) - ( { \frac{1}{ \sqrt{5} } }^{3} )$

$\frac{16}{25} - \frac{1}{ \sqrt{5} }$

${ \huge{ \frac{16 - \sqrt{5} }{25} }}$

${ \green{ \underline{ \underline{ \mathcal{be \: brainly}}}}}$