Question

Evaluate the following:

`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`

Answer 1

We have to find `((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`

Since `
sec 70^@/(cosec 20^@)  + sin 59^@/cos 31^@   sin (90^@ - theta) = cos theta`  and `cos(90^@ - theta) = sin theta`

So

`((sin(90^@ - 41^@))/cos 41^@)^2 + (cos (90^@ - 49^@)/sin 49^@)^2` = `((cos 41^@)/cos 41^@)^2 + ((sin 49^2)/sin 49^@)^2`

= 1 + 1

= 2

So value of `(sin 49^@/cos 41^@)^2 + (cos 41^@/sin 49^@)^@` is 2