Buktikan indetitas trigonometri berikut ini 1. Cot A + Tan A = cot A sec^2 A 2. (Tan A + cot A) cos A sin A - cos^2 A = sin ^2 A 3. Tan A - cot A/tan A + cot

1) cot A + Tan A
= (cos A)/(sin A) + (sin A)/(cos A)
= (cos^2 A + sin^2 A)/(sin A cos A)
= 1/(sin A . cos A)
= 1/(sin A cos A) . (cos A)/(cos A)
= (cos A)/(sin A) . 1/(cos^2 A)
= cot A . sec^2 A

2) (Tan A + cot A) cos A sin A - cos^2 A
= ((sin A)/(cos A) + (cos A)/(sin A)) cos A sin A - cos^2 A
= ((sin^2 A + cos^2 A)/(cos A sin A)) cos A sin A - cos^2 A
= (sin^2 A + cos^2 A) - cos^2 A
= sin^2 A

3) (Tan A - cot A)/(Tan A + cot A)
= (Tan A - 1/(Tan A)) / (Tan A + 1/(Tan A))
= ((tan^2 A - 1)/(Tan A)) / ((tan^2 A + 1)/(Tan A))
= (tan^2 A - 1) / (tan^2 A + 1)
= ((sin^2 A)/(cos^2 A)) - 1) / ((sin^2 A)/(cos^2 A) + 1)
= ((sin^2 A - cos^2 A)/(cos^2 A)) / ((sin^2 A + cos^2 A)/(cos^2 A))
= (sin^2 A - cos^2 A)/(sin^2 A + cos^2 A)
= (1 - cos^2 A - cos^2 A) / 1
= 1 - 2 cos^2 A

Gak jelas tanyaa. . . . . . . . . .