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Answer 1 · 2018-01-06T12:25:47

Qn 3 (a) #x = 11.537^0, -30^0#

Qn 3 (c) #x = 30^0, 150^0, 90^0, -90^2#

Qn 4 (a) # a = 81, A = 43, b = 62, B = 31, c = 114.2, C = 106#

Qn 3 (a)
#10cos^2x+ 3sinx - 9 = 0#

#10 (1-sin^2x) + 3sinx - 9 = 0#

#-10sin^2x + 3sinx + 1 = 0#

#-10sin^2x - 5sinx + 2sinx + 1 = 0#

#-5sinx(2sinx +1) + 1(2sinx + 1) = 0#

#(1-5sinx)(2sinx+1) = 0#

#sinx = 1/5, -1/2)#

#x = 11.537^0, -30^0#

Qn 3 (c)

#2sin^3x - sin^2x - 2sinx + 1 = 0#

#sin^2x(2sinx -1) - 1(2sinx -1) = 0#

#(sin^2x-1)(2sinx-1) = 0#

#sin^2x = 1, sinx = +-1, x = 90^0, -90^0#

#2sinx = 1, x = 30^0, 150^0#

Qn 4 (a)
Given #A = 43^0, a = 81, b = 62#

#a / sin A = b / sin B = c / sin C#

#81 / sin 43 = 62 / sin B#

#sin B = (62/81) * sin 43 = 0.522#

#/_B = sin^-1 0.522 = 31.4665 ~~ 31^0#

#/_C = 180 - /_A - /_B = 180 - 43 - 31 = 106^0$

#81 / sin 43 = c / sin 106#

#c = (81*sin 106) / sin 43 = 114.1677 ~~114.2#

#.a = 81, A = 43, b = 62, B = 31, c = 114.2, C = 106#