高専の数学解説

第12章 12.1

(1)

sin⁡θ+tan⁡θ1+cos⁡θ=sin⁡θ+sin⁡θcos⁡θ1+cos⁡θ=sin⁡θcos⁡θ+sin⁡θcos⁡θ(1+cos⁡θ)=sin⁡θ(1+cos⁡θ)cos⁡θ(1+cos⁡θ)=sin⁡θcos⁡θ\frac{\sin\theta+\tan\theta}{1+\cos\theta}=\frac{\sin\theta+\dfrac{\sin\theta}{\cos\theta}}{1+\cos\theta}=\frac{\sin\theta\cos\theta+\sin\theta}{\cos\theta(1+\cos\theta)}=\frac{\sin\theta(1+\cos\theta)}{\cos\theta(1+\cos\theta)}=\frac{\sin\theta}{\cos\theta}

(2)

tan⁡2θ+1tan⁡θ=sin⁡2θ+cos⁡2θcos⁡2θsin⁡θcos⁡θ=1sin⁡θcos⁡θ\frac{\tan^2\theta+1}{\tan\theta}=\frac{\sin^2\theta+\cos^2\theta}{\cos^2\theta\dfrac{\sin\theta}{\cos\theta}}=\frac{1}{\sin\theta\cos\theta}

解説: r31bn1z