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kiran venkatesh Grade: 11
        

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

7 years ago

Answers : (1)

AJIT AskiitiansExpert-IITD
68 Points
										

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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All the best.


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Ajit Singh Verma IITD

7 years ago
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