Question

Evaluate tan 35 degree/cot 55 degree +cot 78 degree /tan 12 degree

Answer 1

please find the attachment

Answer 2

$Value \: of \: \frac{tan 35\degree }{cot 55 \degree } + \frac{cot 78\degree }{tan 12 \degree }$

$= \frac{tan (90 - 55)\degree }{cot 55 \degree } + \frac{cot (90 - 12)\degree }{tan 12 \degree }$

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$\blue { We \: know \: that , }$

$\pink { 1 ) tan (90 - A) = cot A }\\\orange { 2) cot (90 - A ) = tan A }$

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$= \frac{cot 55\degree }{cot 55 \degree } + \frac{tan 12\degree }{tan 12 \degree }$

$= 1 + 1 \\= 2$

Therefore.,

$\red{ Value \: of \: \frac{tan 35\degree }{cot 55 \degree } + \frac{cot 78\degree }{tan 12 \degree }}\green {= 2}$

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