Найдите tg²α, если 5sin²α+13cos²α=6

Question

Найдите tg²α, если 5sin²α+13cos²α=6

Answer 1

5(1-cos²α) +13cos²α=6

5-5cos²α+13cos²α=6

8cos²α=1

cos²α=1\8

5sin²α+13(1-sin²α)=6

5sin²α+13-13sin²α=6

-8sin²α=-7

sin²α=7/8

 tg²α=(1/8)/(7/8)=1/7