Is it safe to invest in the US stock market from India?

Yes. Note that while investing in foreign markets comes with its own set of challenges, it does not render it unsafe. However, you need to be aware of currency fluctuations when you are investing in foreign markets. In fact, you may also use this to your advantage. For instance, if the rupee loses value and a portion of your investment is in USD, the value of your investment will rise in terms of INR, which is the currency of your home country. If you cash in your investment, you will get more rupees per dollar as compared to the rate at which you invested. Similarly, if the USD rises, your investment value (in USD) will rise, even if there is no change in your portfolio.