Question

if sinx+cosecx=2
then what is sin^6x+cosec^6x​

Answer 1

Answer:

2

Step-by-step explanation:

$\\\tt \sin \: x + \csc(x) = 2$

Squaring both sides:

$\\\tt { \sin }^{2} x + 2 + { \csc }^{2} x = {2}^{2} \\\tt { \sin }^{2} x + { \csc }^{2} x = 2$

Cubing both sides and substituting values:

$\\\tt { \sin }^{6} x + { \cos }^{6}x + 3( { \sin}^{2} x)( { \csc}^{2} x)( { \sin}^{2} x + { \csc }^{2} x) = 2 ^{3}$

Now,

$\\\tt { \sin }^{6} x + { \cos }^{6}x + 3( 2) = 8 \: \\\tt { \sin }^{6} x + { \cos }^{6}x = 2$