How do you find the exact value of #cos2theta+sin^2theta=1# in the interval #0<=theta<360#?

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Answer 1 · 2016-12-01T16:10:15

In the interval #[0,2pi)# the solutions are #theta =0# and #theta = pi#.

Use the formula for double angle:

#cos(2 theta) = cos^2(theta) - sin^2(theta)#

so that:

#cos(2theta) + sin^2theta =1#

becomes:

#cos^2(theta) - sin^2(theta)+ sin^2theta =1#

#cos^2 theta = 1#

#cos theta =+-1#

In the interval #[0,2pi)# the solutions are #theta =0# and #theta = pi#.