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Question Number 82176 by oyemi kemewari last updated on 19/Feb/20

Commented by jagoll last updated on 19/Feb/20

$$\left(1b\right)\sqrt{32-2\sqrt{135}}=\sqrt{27+5-2\sqrt{27\times 5}}$$$$=\sqrt{27}-\sqrt{5}=3\sqrt{3}-\sqrt{5}$$

Commented by jagoll last updated on 19/Feb/20

$$\left(2b\right)\alpha \times (\alpha +3)=28$$$${\alpha }^2+3\alpha -28=0$$$$(\alpha +7)(\alpha -4)=0$$$$\left(i\right)k=2\alpha +3=-11$$$$\left(ii\right)k=2\alpha +3=11$$

Commented by john santu last updated on 19/Feb/20

$$\frac{\cos x}{1+\sin x}+\frac{1+\sin x}{\cos x}=$$$$\frac{\cos {}^{2}x+1+2\sin x+\sin {}^{2}x}{\cos x(1+\sin x)}=?$$$$\frac{2(1+\sin x)}{\cos x(1+\sin x)}=\frac{2}{\cos x}=2\sec x$$

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