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If s in x+cos e c\ x=2, then write the v...

If `s in x+cos e c\ x=2,` then write the value of `sin^n x+cos e c^n xdot`

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`sin A+ "cosec" A=2`
`rArr sin A + 1/(sin A)=2`
`rArr sin^(2)A+1=2 sinA`
`rAr sin^(2)A-2sinA+1=0`
`rArr (sinA-1)^(2)=0`
`rArr (sin A-1)^(2)=0`
`rArr sinA=1`
`therefore` L.H.S`=sin^(n)A + "cosec"^(n)A`
`=sin^(n)A + 1/(sin^(n)A)= 1^(n)+1/n^(n)`
`=1+1=2= R.H.S` Hence proved.
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