How do you find the general solutions for #sin theta - cos theta = 1#?

1 Answer
Nghi N.
Aug 17, 2015

Solve sin x - cos x = 1

Ans: #pi and pi/2#

Explanation:

Apply the trig identity: #sin x - cos x = sqrt2.sin (x - pi/4)#

#sqrt2sin (x - pi/4) = 1#
#sin (x - pi/4) = 1/sqrt2 = sqrt2/2#
Trig table gives -->
#(x - pi/4) = pi/4# and #(x - pi/4) = (3pi)/4#

a. #x - pi/4 = pi/4 #--> #x = (2pi)/ 4 = pi/2#

b. #x - pi/4 = 3pi/4# --> #x = (3pi)/4 + pi/ 4 = pi#
Check
#x = pi/2# --> #sin (pi/2) - cos (pi/2) = 1 #OK

#x = pi# --> #sin pi - cos pi = 1# --> 0 - (-1) = 1 OK

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