sec^2 x + 2tan x = 6sec2x+2tanx=6
1/(cos^2 x) + (2sin x)/(cos x) = 61cos2x+2sinxcosx=6
1 + 2sin x.cos x = 6cos^2 x1+2sinx.cosx=6cos2x
Use trig identities:
sin 2x = 2sin x.cos x
2cos^2 x = 1 + cos 2x2cos2x=1+cos2x
In this case we have:
1 + 2sin x = 3 + 3cos 2x1+2sinx=3+3cos2x
2sin 2x - 3cos 2x = 22sin2x−3cos2x=2
sin 2x - (3/2)cos 2x = 1sin2x−(32)cos2x=1
Call tan t = sin t/(cos t) = 3/2 = tan 56^@31tant=sintcost=32=tan56∘31, we get:
sin 2x.cos t - sin t.cos 2x = cos 56^@31 = 0.55sin2x.cost−sint.cos2x=cos56∘31=0.55
sin (2x - 56.31) = 0.55
Use calculator and unit circle -->
a. (2x - 56.31) = 33^@68(2x−56.31)=33∘68
2x = 33.68 + 56.32 = 90^@ --> x = 45@x=45∘
b. (2x - 56.31) = 180 - 56.31 = 123^@69
2x = 123.69 + 56.31 = 180^@ --> 2x=123.69+56.31=180∘−→x = 90^@#
