Question

wykaz ze jesli alfa jest katem ostrym i 2 cos do kwadratu alfa + 5sin kwadrat alfa = 4, to (tg alfa+ ctg alfa ) do kwadratu=4,5. Prosze pomocyy :(

Answer 1

Answer 2

α∈(0°;90°)

2cos²α+5sin²α=4

 

2cos²α+2sin²α+3sin²α=4

2(cos²α+sin²α)+3sin²α=4

3sin²α+2=4

3sin²α=2

sin²α=²/₃

sinα=√6/₃

 

sin²α+cos²α=1

²/₃+cos²α=1

cos²α=¹/₃

cosα=√3/₃

 

tgα=sinα/cosα=√2

ctgα=1/tgα=√2/₂

 

(tgα+ctgα)²=(1,5√2)²=⁹/₂=4,5