Question

Solve the above question

Answer 1

Tan(½cos-1(√5/3))
Let (½cos-1(√5/3)=x
cos-1(√5/3)=2x
(√5/3)=cos 2x
(√5/3)=1-tan²x/1+tan²x
√5 +√5tan²x= 3- 3tan²x
√5tan²x + 3tan²x= 3 - √5
= 3 + √5(tan²x)= 3 - √5
Tan²x = 3 - √5/ 3 + √5
On rationalising we get
Tan²x =( 3 - √5)2/9-5
Tan²x =( 3 - √5)2/4
Tan x =( 3 - √5)/2
 x =tan-1( 3 - √5)/2
now Tan(½cos-1(√5/3))
=tan x
=tan(tan-1( 3 - √5)/2)
= ( 3 - √5)/2=ans