Question

If sin x + cosec x = 2, then what is sinx + cosec20x ?
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Answer 1

sinx+cosecx=2

⇒sin x + 1/sin x = 2

⇒ sin² x + 1 = 2 sin x

⇒sin² x – 2 sin x + 1 = 0

⇒(sin x – 1) ² = 0

⇒sin x = 1

cosec x = 1

sin¹ⁿx+cosec¹ⁿ x=2

Hope it helps you.

Answer 2

Answer:

$Given, sinX+cosecX=2\\\\sinX+\frac{1}{sinX} =2\\\\\frac{sin^{2}X+1 }{sinX} =2\\\\ sin^{2}X+1=2sinX\\ sin^{2}X+1-2sinX=0\\ (sinX-1)^{2} =0\\(sinX-1)=0\\sinX=1\\sinX=sin90°\\X=90°\\\\Now,sin^{19}X+cosec^{20}X\\ (sin 90°)^{19} +(cosec90°)^{20} \\(1)^{19} +(1)^{20}\\ 1+1\\2$