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Question
Evaluate the following :
`((sin 49^@)/(cos 41^@))^2 + (cos 41^@/(sin 49^@))^2`
Solution
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
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