trigno question ....

putting value of A 45° we get
l.h.s
1/8-1/8=..
r.h.s
(1/2-1/2)(,...)=0';;;;
i.e qstn is crrct

a³ - b³ = (a-b)(a² + ab - b²)
put a as sinA and b as cosA.
sin³a - cos³a = (sinA - cosA)(1 - sinA*cosA).
and it is given that this is equal to (sinA - cosA)(sinA + cosA)(sin⁴A + cos⁴A)
and as far as i can see these are not equal.
put a = 30 degrees.
and then LHS = 1/8 - 3*root3/8.
RHS = (1/4 - 3/4)(1 - 2*1/4*3/4) = -1/2(5/8) = -5/16.
HENCE LHS ≠RHS.