India is a Tropical country but has a Monsoonal climate because

The whole of India, south of the Himalayas can be climatically treated as a tropical country as the Himalayas provide the barrier effect. 

Indian subcontinent is separated from the rest of Asia by the lofty Himalayan ranges which block the cold air masses moving southwards from Central Asia.

 As a result, during winters, the northern half of India is warmer by 3°C to 8°C than other areas located on same latitudes.

During summer, due to over the head position of the sun, the climate in the southern parts resemble equatorial dry climate.

The seasonal reversal of winds in Arabian Sea and Bay of Bengal give India a typical tropical monsoon climate.

So Indian climate, to be precise, is Tropical monsoon type (a distinct wet and dry climate) rather than just a tropical or half temperate climate.