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Solve the given triginometric equation analytically

sin4x - cos2x = 0

Priya

2 answers

let's use the identity
sin2A = 2sinAcosA on the first term only

2sin2xcos2x - cos2x = 0 , now a common factor

cos2x(2sin2x - 1) = 0
cos2x = 0 or sin2x = 1/2

so 2x = 90, 270, 30, 150º
then x = 45,135,15,75º

but the period of sin2x and cos2x is 180º

so other answers are 225,315,195º

to change these quickly to radians, take the smallest degree angle which is 15º
15º = pi/12 radians
all other angles are multiples of 15
eg. 315 = 21*15
so 315º = 21pi/12 etc.
Given angle 1 = (x + 7)degree, angle 2 = *(2x -3)degree, angle ABC = (x 2nd power) degree, angle D = (5x - 4)degree. Show that angle ABC congruent to angle D