Question

Evaluate sin(2 tan inverse 1/4) +cos(tan inversr 2root2)

Answer 1

Answer:

Step-by-step explanation:

let tan^-1 1/4= Q

tan Q=1/4...(1)

now sin(2tan^-1 1/4)= sin 2Q

     

                                      = 2tanQ/1+tan^2Q

                                      = 2*1/4/1+(1/4)^2

                                      =1/2/1+1/16

                                       =1/2/17/16

                                        =1/2*16/17

now solving

cosQ(tanQ^-1 2root 2)

therefore tanQ= 2root2

and we need to find \

cosQ(tanQ^-1 2root 2)=cosQ

we know that

1+tan^2Q=sec^2Q

1+(2root2)^2=sec^2Q

1+8=sec^2Q

sec^2Q=9

1/cos^2Q=9

cosQ=+-1/3

since value of tan is positive

we take positive value of cosQ

therefore, cosQ=1/3

so, cosQ(tanQ^-1 2root 2)=1/3

now,

sin(2 tan inverse 1/4) +cos(tan inversr 2root2)

=8/17*1/3

41/51