Math, asked by amitbobbypathak, 6 hours ago

if the period of the function f(x)= sin^4x -cos^4x is mπ/n where m and n are co prime then find the value of (mn)^2​

Answers

Answered by pulakmath007
11

SOLUTION

GIVEN

The period of the function

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

is mπ/n where m and n are co prime

TO DETERMINE

The value of (mn)²

EVALUATION

Here the given function is

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

We simplify it as below

 \sf{f(x) = ( { \sin}^{2} x  +   { \cos}^{2}x)({ \sin}^{2} x -  { \cos}^{2}x) }

 \sf{ \implies \: f(x) = 1.({ \sin}^{2} x -  { \cos}^{2}x) }

 \sf{ \implies \: f(x) = ({ \sin}^{2} x -  { \cos}^{2}x) }

 \sf{ \implies \: f(x) = -  ({ \cos}^{2} x -  { \sin}^{2}x) }

 \sf{ \implies \: f(x) = -   \cos2x  }

So period of f(x) = π

Now it is given that the period of f(x) is mπ/n

Thus we have m = 1 , n = 1

Therefore (mn)²

= (1 × 1)²

= 1

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