Question

Plz answer the qs which is in the attachment...

Answer 1

$Given : \frac{sin^4x}{2} + \frac{cos^4x}{3} = \frac{1}{5}$

$= \ \textgreater \ 3sin^4x + 2cos^4x = \frac{6}{5}$

$= \ \textgreater \ 3sin^4x + 2(1 - sin^2x)^2 = \frac{6}{5}$

$= \ \textgreater \ 3sin^4x + 2(1 + sin^4x - 2sin^2x) = \frac{6}{5}$

$= \ \textgreater \ 3sin^4x + 2 + 2sin^4x - 4sin^2x = \frac{6}{5}$

$= \ \textgreater \ 5sin^4x - 4sin^2x + 2 = \frac{6}{5}$

$= \ \textgreater \ 25sin^4x - 20sin^2x + 10 = 6$

$= \ \textgreater \ 25sin^4x - 20sin^2x + 4 = 0$

$= \ \textgreater \ (5sin^2x - 2)^2 = 0$

= > 5sin^2x = 2

= > sin^2x = 2/5.


Then,

cos^2x = 1 - sin^2x

             = 1 - (2/5)

             = 3/5.



Now,

=  >tan^2x = sin^2x/cos^2x

                  = (2/5) * (5/3)

                  = 2/3.



Now,

$= \ \textgreater \ \frac{sin^8x}{8} + \frac{cos^8}{27}$

$= \ \textgreater \ \frac{(sin^2)^4x}{8} + \frac{(cos^2x)^4}{27}$

$= \ \textgreater \ \frac{( \frac{2}{5})^4 }{8} + \frac{( \frac{3}{5})^4 }{27}$

$= \ \textgreater \ \frac{ \frac{16}{625} }{8} + \frac{ \frac{81}{625} }{27}$

$= \ \textgreater \ \frac{16}{5000} + \frac{16}{16875}$

$= \ \textgreater \ \frac{5}{625}$

$= \ \textgreater \ \frac{1}{125}$



Therefore, Option(A), Option(B) are correct.


Hope this helps!