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Number of solution(s)of the equation sin2A + cos2A = -1/2 ; A belongs in range[0,pi/2] (a)0 (b)1 (c)2 (d)3 please provide the step-wise solution

Number of solution(s)of the equation  sin2A + cos2A = -1/2 ; A belongs in range[0,pi/2]
(a)0 
(b)1
(c)2
(d)3
please provide the step-wise solution

Grade:11

1 Answers

waqar malik
14 Points
4 years ago
squaring on both sides we get..
1+2sin2Acos2A=1/4
(since, 2sinAcosA=sin2A)
therefore, 1+sin4A=1/4
again,            sin4A=-3/4….….….(1)
Since , A ~[0, pi/2]
Therefore, 4A~[0, 2pi]
from equation 1 it is clear that angle 4A will be in 3rd or 4th quadrant,
Hence the equation has only 2 solutions.

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