यदि ` sin A + "cosec"A = 2` तो सिद्ध कीजिए कि -` sin^(n) A + "cosec"^(n) A =2`

Explanation

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