Sinxcosx=1/2√2?

sinxcosx=1/2√2

1 Answer
Jun 12, 2018

pi/4; (3pi)/4π4;3π4

Explanation:

sin x.cos x = 1/(2sqrt2) sinx.cosx=122
(sin 2x)/2 = 1/(2sqrt2)sin2x2=122
sin 2x = 1/sqrt2 = sqrt2/2sin2x=12=22
Trig table and unit circle give 2 solutions for x -->
x = pi/4x=π4, and x = (3pi)/4x=3π4
General answers:
x = pi/4 + 2kpix=π4+2kπ, and
x = (3pi)/4 + 2kpix=3π4+2kπ