Question

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

Answer 1

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

Answer 2

Step-by-step explanation:

sin x +cosec x =2

sin x+1/ sin x=2

sin²x+1=2sin x

sin²-2sinx+1=0

in form of (sinx-1)²

(sin x-1)²=0

sin x -1=0

sin x=1

x is 90°

cosec x =1

cosec 20 x= 20(1)=20

sin x + cosec 20 x =20+1

=21