Question

Evaluate: tan[1/2
cos-1(3/√11)
]
​

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

got this from Google survey you can figure out by this

Answer 2

Answer:

Step-by-step explanation: