Question

if
${cos}^{100} x - {sin}^{100} x = 1$
then x=?

...


answer me​

Answer 1

Answer:

sin

100

x−cos

100

x=1

sin

100

x=1+cos

100

x

We know that ,

−1≤sinx≤1−1≤cosx≤1

0≤sin

100

x≤10≤cos

100

x≤1

Now,

max value of sinx=1minvalueof1+cosx=1

sinx=1

sin

100

x=(sin

2

x)

50

=(±1)

2

=1

=sin

2

π

Hence general solution is x=nπ+

2

π