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FIND ALL ANGLES LYING BETWEEN 0DEGREE AND 360DEGREE SATISFYING 1) 2cos 2 A-sinA-1=0 2) 4cot 2 A=3cosec 2 A 3)sin 4 A-2sin 2 A=1 4)3(sec 2 A+tan 2 a)=5

FIND ALL ANGLES LYING BETWEEN 0DEGREE AND 360DEGREE SATISFYING


1) 2cos2A-sinA-1=0


2) 4cot2A=3cosec2A


3)sin4A-2sin2A=1


4)3(sec2A+tan2a)=5

Grade:11

1 Answers

AJIT AskiitiansExpert-IITD
68 Points
11 years ago

Dear  kiran ,

1) 2(1- sin2A) -sinA -1 =0 

    2(1-sin2A))  = sinA + 1

   cancelling we get , sinA +1  = 0 ---not possible or 1 - sin2A =1/2 i.e sin2A = 1/2

so , sinA = ±(1/2)0.5   , we get A= 45, 135 , 225 , 315

2) 4 cot2A = 3 cosec2A  

   4 cos2A =  3  ;  cosA =±  30.5/ 2   , we get A =  30  , 150 , 210 ,330

3)put sin2A = t ,  t2 -2t -1 = 0  solving we get , t  = 1± √2    ; both are not possible . so no solution

4) 3( 1+ sin2A)  = 5 cos2

    3( 1+ sin2A)  = 5 (1- sin2A)

    8sin2A  = 2 

       sin2A  = 1/4

        sinA = ± 1/2

we get A  =  30  , 150 , 210 ,330

 

 

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