Answer :



sin x + 1 = 2 × (cos x)2


sin x + 1 = 2 × (1 - (sin x)2)


sin x + 1 = 2 – 2(sin x)2


2(sin x)2 + sin x - 1 = 0


Consider a=sin x


So, the equation will be


2a2+a-1=0


From the equation a=0.5 or -1


Which implies


Sin x=0.5 or sin x=(-1)


Therefore x=30° or 270°


But for x=270° our equation will not be defined as cos (270° )=0


So, the solution for x=30°


According to trigonometric equations


If sin x=sin a


Then x=nπ – na


Here sin x=sin30


So, x=nπ + (-1)n × 30


For n=0, x=30 and n=1,x=150° and for n=2,x=390


Hence between 0 to 2π there are only 2 possible solutions.


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