Question

Comprove a identidade trigonométrica:

cos x (2 + tg x) (2tgx + 1) = 2sec x + 5sen x​

Answer 1

cos x .(4 tg x + 2 + 2 tg ² x + tg x) = 2/ cos x + 5 sen x

cos x .(2 tg ² x + 5 tg x + 2 ) = 2 + 5 sen x.cos x / cos x

(2 tg ² x + 5 tg x + 2 ) = 2 + 5 sen x.cos x / cos ² x

(2 sen ² x / cos ²x) + (5 sen x/ cos x) + 2 = 2 + 5 sen x.cos x / cos ² x

(2 sen ² x+ 5 sen x. cos x + 2 cos ² x)/ cos ² x = 2 + 5 sen x.cos x / cos ² x

RTF: sen ² + cos ² = 1 ⇒ 2 sen ² + 2 cos ² x = 2 ∴

(2 + 5 sen x.cos x)/ cos ² x = (2 + 5 sen x.cos x)/ cos ² x

2 + 5 sen x. cos x = 2 + 5 sen x.cos x

5 sen x.cos x = 5 sen x.cos x

sen x.cos x = sen x.cos x

sen x = sen x rsrsrs...