Question
Sun July 22, 2012 By: Chethan U

if cosecA+cotA=11/2 Find tanA

Expert Reply
Sun July 22, 2012
Answer : Given : cosecA+cotA=11/2
To Find : tanA
 
=> cosecA + cotA = 11 / 2
=> (1/sinA ) + (cosA / sinA) = 11/2 {using cosecA = 1/sinA and 
                                                        cotA = cosA /sinA }
 
=>(1+cosA) / sinA = 11/2
=> 2cos2(A/2) / 2 sin(A/2)cos(A/2) = 11/2 {using 1+ cos 2A = 2cos2
                                                               ans sin2A = 2sinA cosA }
 
=> cos(A/2) / sin(A/2) = 11/2    
=>cot(A/2) = 11/2                    {using cotA = cosA/sinA}
=>tan(A/2) = 2/11                    { using tanA = 1/cotA }
 
Now using tan2A = 2tanA /( 1 - tan2A),we get 
=> tanA = 2tan(A/2) / ( 1 - tan2(A/2))
=> tanA =( 2* (2/11)) / ( 1 - (2/11)2 )
=> tanA = (4/11) / (1 - (4/121) )
=> tanA = (4/11) / (117/121)
=>tanA = 44 / 117 Answer  
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