Question

prove that.:– Cos^4 – cos^2 = sin^4 – sin^2

Answer 1

Heya user,

We use sin²Ф + cos²Ф = 1;

cos²Ф ( cos²Ф - 1 )
= [ 1 - sin²Ф ] [ - sin²Ф ]
= sin²Ф [ sin²Ф - 1 ]  <---- Which is equal to desired result;

Answer 2

hello users .....

solution:-
we have to prove that:
cos⁴x - cos²x = sin⁴x - sin²x

we know that ;
(1 - sin²x) = cos²x
and
(1 - cos²x) = sin²x

here,
taking LHS...
cos⁴x - cos²x
= cos²x(cos²x - 1)
= - cos²x (1 - cos²x)
= - sin²x cos²x

Now,
taking RHS....
sin⁴x - sin²x
= sin²x( sin²x - 1)
= - sin²x (1 - sin²x)
= -sin²x cos²x

Hence;
LHS= RHS. proved ..

✡⭐ Hope it helps ✡⭐