Verify this identity in Trig?
Hopefully that isn't confusing. Step by step, please!
- Seamus OLv 79 years agoFavorite Answer
each bit on the LHS can be simplified first using co-function identities then put together to get the RHS
3π/2 + x is in quadrant 4 ... so sin [(3π/2) + x] = -cos x
and 3π/2 - x is in quadrant 3 ... so sin [(3π/2) - x] = -cos x
so sin [(3π/2) + x] + sin [(3π/2) - x] = -cos x - cos x
= -2cos x
btw ... just in case you're wondering why sin [(3π/2) + x] = -cos x and NOT cos x ... it's b/c sine is negative in quadrant 4 and that determines the sign of the co-function ... gotta be careful about that