Question

The value of the angle tan–1(tan65° – 2 tan 40°) in degrees, (as tan–1(tan x°) = x°) is equal to Answer:

Answer 1

Answer:

I don't know this answer

Answer 2

Answer:

25°

Step-by-step explanation:

$tan^{-1}$(tan65° – 2 tan 40°)

= $tan^{-1}$(tan65° –  tan 40°-tan 40°

= $tan^{-1}$(tan(65°-40°) (1+ tan(65°)tan (40°))-tan (40°))

we know (tan(A−B)(1+tanAtanB)=tanA−tanB)

= $tan^{-1}$(tan(25°) + tan(25°)tan(65°)tan (40°)-tan (40°))

= $tan^{-1}$(tan(25°) + tan(25°)cot(25°)tan (40°)-tan (40°))

= $tan^{-1}$(tan(25°) + tan (40°)-tan (40°))

= $tan^{-1}$(tan(25°))

=25°