Question

सिद्ध कीजिए कि `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`

Answer 1

हमें प्राप्त है:

`(sec8 theta - 1)/(sec4 theta - 1) = ((1 - cos8 theta) cos 4theta)/((1 - cos4theta)cos 8theta)`

= `(2sin^2 4theta cos 4theta)/(cos8theta 2sin^2 2theta)`  

= `(sin4theta(2sin4theta cos 4theta))/(2cos8theta sin^2 2theta)`

= `(sin4theta sin 8theta)/(2 cos8 theta sin^2 2theta)`  

= `(2sin 2theta cos 2theta sin 8theta)/(2 cos8theta sin^2 2theta)`

= `(tan8 theta)/(tan 2theta)`