No, you cannot deduct state income taxes applied to your investments on line 9b of Form 8960 if you took the standard deduction. Here's a concise summary:
Standard Deduction: If you take the standard deduction, you cannot itemize deductions, including state income taxes.
Form 8960: Line 9b allows deductions for state, local, and foreign income taxes only if they are properly deducted on your income tax return, which requires itemizing