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Question Number 57448 by Pk1167156@gmail.com last updated on 04/Apr/19

$$\mathrm{If}\sin x+\mathrm{cosec}x=2,\mathrm{then}{\sin }^{n}x+{\mathrm{cosec}}^{n}x$$$$\mathrm{is}\mathrm{equal}\mathrm{to}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 04/Apr/19

$$a+\frac{1}{a}=2$$$$a^2+1=2a$$$${(a-1)}^2=0soa=1$$$$sinx=a=1$$$$cosecx=\frac{1}{a}=1$$$${sin}^{n}x+{cosec}^{n}x$$$${\left(1\right)}^n+{\left(1\right)}^n$$$$=2$$

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