Function x=A sin2 ωt+B cos2 ωt+C sin ωt cos ωt  represents SHM :(i) for any value of A, B and C (except C = 0)(ii) if A=- B; C = 2B, amplitude = B2(iii) if A = B; C = 0(iv) if A = B; C = 2B, amplitude=B

x=A sin2ωt+B cos2ωt+C sinωt cosωt x=A21-cos 2ωt+B21+cos 2ωt+C2sin 2ωtFor (a) : For any value of A, B and C (except C = 0), it represents SHMFor (b) : If A = -B and C = 2B, , x = B cos ωt + B sin 2 ωt which is SHM.For (c ): If A=B,C =0, x= A = constant ⇒Not a SHM.For (d) : If A=B,C =2B, x = B+B sin 2 ωt which is SHM.