Question

If sin4 θ – cos4 θ =k4 ,then sin2 θ – cos2 θ =______​

Answer 1

Answer:-

Given that,

$\sf { \sin}^{4} (x) - { \cos}^{4} (x) = {k}^{4}$

$\sf \implies{( \sin}^{2} (x) - { \cos}^{2} (x) )( { \sin }^{2}(x) + { \cos}^{2}(x)) = {k}^{4}$

Now,

we know that,

$\sf { \sin }^{2}(x) + { \cos}^{2}(x) = 1$

So,

$\sf \implies{( \sin}^{2} (x) - { \cos}^{2} (x) ) \times 1 = {k}^{4}$

$\sf \implies{\sin}^{2} (x) - { \cos}^{2} (x)= {k}^{4}$

Which is the required answer.

Answer 2

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