Question

Buktikan identitas trigonometri :
a. sin D cos D sec D csc D = 1
b. (sin A + cos A)^2 - 2 tan A cos^2 A = 1
c. sin^4 A - cos^4 A = 1 - 2 cos^2 A
d. cot A + tan A = cot A sec^2 A

^ = pangkat
Jawab lengkap ya ^^

Answer 1

A.
sin.cos.sec.csc = 1
sin.cos.1/cos.1/sin = 1
cos/cos.sin/sin = 1
1.1 = 1
1 = 1

b. (sin + cos)^2 - 2.tan.cos^2 = 1
sin^2 + 2.sin.cos + cos^2 - 2.(sin/cos). cos^2 = 1
sin^2 + cos^2 - 2.sin.cos - 2.sin.cos = 1
sin^2 + cos^2 = 1
1 = 1

c. sin^4 - cos^4 = 1 - 2.cos^2
sin^2.sin^2 - cos^4 = 1 - 2.cos^2
(1 - cos^2)(1 - cos^2) - cos^4 = 1 - 2.cos^2
1 - 2.cos^2 + cos^4 - cos^4 = 1 - 2.cos^2
1 - 2.cos^2 = 1 - 2.cos^2

d.cot + tan = cot.sec^2
cos/sin + sin/cos = cot.sec^2
(cos^2 + sin^2)/(sin.cos) = cot.sec^2
1/(sin.cos) = cot.sec^2
sin.sec = cot.sec^2
cot/cos . sec = cot.sec^2
cot.sec.sec = cot.sec^2
cot.sec^2 = cot.sec^2

kalo masih bngung boleh ditanyakan :)