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Question
Evaluate:
`2(tan35^@/cot55^@)^2 + (cot55^@/tan35^@)^2 - 3(sec40^@/(cosec50^@))`
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Solution
`2(tan35^@/cot55^@)^2 + (cot55^@/tan35^@)^2 - 3(sec40^@/(cosec50^@))`
= `2(tan(90^@-55^@)/cot55^@)^2 + (cot(90^@-35^@)/tan35^@)^2 - 3(sec(90^@-50^@)/(cosec50^@))`
= `2(cot55^@/cot55^@)^2 + (tan35^@/tan35^@)^2 - 3((cosec50^@)/(cosec50^@))` ...`[∵ tan (90^@ - theta) = cot theta` `cot(90^@ - theta) = tan theta` ` sec(90^@ - theta) = cosec theta`]
= 2 × (1)2 + (1)2 – 3 × 1
= 2 × 1 + 1 – 3
= 2 + 1 – 3
= 0
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