if cosecA+cotA=11/2 Find tanA

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 = 2cos²A 

                                                               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