>>506
(1)x^2-y^2 = (x+y)(x-y) を使う

(tan(θ)+cos(θ))^2 - (tan(θ)-cos(θ))^2
= 2tan(θ)*2cos(θ) = 4sin(θ)

(2) 1+sin(θ) を分子・分母に掛ける

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