Question

求证：(secx)^6-(tanx)^6=1+3(secx)^2(tanx)^2

Answer 1

证明过程如下：

sinx^2+cosx^2=1

(sinx^2+cosx^2)^3=1^3=1

(sinx^2)^3+3sinx^4cosx^2+3sinx^2cosx^4+(cosx^2)^3=1

sinx^6+3sinx^2cosx^2(sinx^2+cosx^2)+)^3=1

1-sinx^6=cosx^6+3sinx^2cosx^2(两边同时除以cosx^6)

1/cosx^6-sinx^6/cosx^6=1+3(1/cosx^2)(sinx^2/cosx^2)

(secx)^6-(tanx)^6=1+3(secx)^2(tanx)^2 证毕!