Question

Buktikan bahwa: sec⁴B - sec²B = tan⁴B + tan²B

Answer 1

Sec^4 B - sec^2 B = tan^4 B + tan^2 B
sec^2 B (sec^2 B - 1) = tan^4 B + tan^2 B
(1 + tan^2 B)(1 + tan^2 B - 1) = tan^4 B + tan^2 B
(1 + tan^2 B)(tan^2 B) = tan^4 B + tan^2 B
tan^2 B + tan^4 B = tan^4 B + tan^2 B
tan^4 B + tan^2 B = tan^4 B + tan^2 B (terbukti)