Question

2 tan^-1 (1/5) + Sec ^-1 (5root2/7)+2tan^-1 (1/8)

Answer 1

Taking first and third

2(tan inverse 1/5 + tan inverse 1/ 8) + sec inverse (5 root 2/7)

 

2(tan inverse [( 1/5+1/8) / 1-(1/5)*(1/8) ]+sec inverse (5 root 2/7)

2( tan inverse [ 13/39]+sec inverse (5 root 2/7)

2(tan inverse [1/3])+ sec inverse (5 root 2/7)

tan inverse [ (2*1/3)/(1-(1/3)*(1/3) ] + sec inverse (5 root 2/7)   [Using formula ]

tan inverse [ (6/9)/(8/9) ] +sec inverse (5 root 2/7)

tan inverse [ 3/4] + sec inverse (5 root 2/7)

now , sec inverse (5 root 2/7) can be converted to tan using a triangle

tan inverse 1/7

now, tan inverse [3/4]+tan inverse [1/7]

using formula

tan inverse [(3/4+1/7)/(1-(3/4*1/7)]

tan inverse [ 25 / 25]

tan inverse [ 1 ]

= pi/4 = 45 degree