Evalute tan⁡α−cot⁡αsin4α−cos4α if α is an acute angle and tan⁡α=2

feminizmiki

feminizmiki

Answered

2022-01-16

Evalute tanαcotαsin4αcos4α if α is an acute angle and tanα=2

Answer & Explanation

RizerMix

RizerMix

Expert

2022-01-20Added 437 answers

Hints: tana=1cota cos2a=11+tan2a and sin2a=11+cot2a
Vasquez

Vasquez

Expert

2022-01-20Added 457 answers

With openspaces
user_27qwe

user_27qwe

Expert

2022-01-23Added 230 answers

Factorizing the denominator and using the fact that sin2a+cos2a=1, we have tanαcotαsin4αcos4α=tanαcotαsin2αcos2α=sec2αtanαcotαtan2α1=(tan2α+1)tanαtanαtan2α1 =(4+1)(212)41=52

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