Question

(tan57° + cot37°)/ (tan33° + cot53° ) =?

• A. sin53° + cos33°
• B. tan53°× tan57°
• C. sin53° × sin57°
• D. cos57° × cos53°

Answer 1

Answer:

B. tan53°× tan57°

Solution: Given: (tan57° + cot37°)/ (tan33° + cot53°) We know cot(A) = tan(90-A)​ So, [tan 33° = cot 57° and cot37° = tan 53° ] ⇒ (tan57° + tan 53°) / (cot 57° + cot 53°) ⇒ (tan57° + tan 53°) / (1/tan 57° + 1/tan 53°) ⇒ (tan57° + tan53°) / {(tan53° + tan57°)/tan53°× tan57°} ⇒ tan53° × tan57°