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Question
Evaluate without using trigonometric tables.
`2((tan 35^@)/(cot 55^@))^2 + ((cot 55^@)/(tan 35^@)) - 3((sec 40^@)/(cosec 50^@))`
Solution
`2((tan 35^@)/(cot 55^@))^2 + ((cot 55^@)/tan 35^@)^2 - ((sec 40^@)/(cosec 50^@))`
`= 2((tan (90^@ - 55^@))/cot 55^@)^2 + ((cot(90^@ - 35^@))/tan 35^@)^2 - 3((sec (90^@ - 50^@))/(cosec 50^@))`
`= 2((cot 55^@)/(cot 55^@))^2 + ((tan 35^@)/(tan 35^@))^2 - 3((cosec 50^@)/(cosec 50^@))` [∵ `tan (90^@ - theta) = cot theta` `cot(90^@ - theta) = tan theta` ` sec(90^@ - theta) = cosec theta`]
`= 2(1)^2 + (1)^2 - 3(1)`
= 2 + 1 - 3
= 0
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