If # sinx+cosx = 1/2 # find #sin2x#?

Question

5181 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-24T16:05:04

#sin2x = -3/4#

Given that:

# sinx+cosx=1/2 #

Then:

# (sinx+cosx)^2 = (1/2)^2 #
# :. sin^2x + 2sinxcosx + cos^2x = 1/4 #

But we know that:

# sin2-= 2sinxcosx \ \ # and # \ \ sin^2x+cos^x -=1#

Hence we have:

# 1+sin2x = 1/4 => sin2x = -3/4#