for the first one , send sin^4 (x) to L.H S and then use the identity ( a^2 - b^2 ) = (a+b)(a-b)
you will have the answer in 2 steps literally..
For second one , Add -1 on both sides , leave RHS Untouched.. On LHS , Substitute 1 as sin^2 (x) + cos^2(x) and starting solving by taking common and condensing repeatedly..