(sec^2 B - 1)(cot^2 B + 1) = sec^2 B

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justaguide | College Teacher | (Level 2) Distinguished Educator

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It has to be shown that `(sec^2 B - 1)(cot^2 B + 1) = sec^2 B`

`(sec^2 B - 1)(cot^2 B + 1)`

=> `(sec^2 B*cot^2 B + sec^2 B - cot^2 B - 1`

=> `(1/(cos^2B))*(cos^2B)/(sin^2B) + 1/(cos^2B) - (cos^2B)/(sin^2B) - 1`

=> `1/(sin^2B) + 1/(cos^2B) - (cos^2B)/(sin^2B) - 1`

=> `(sin^2B)/(sin^2B) + 1/(cos^2B) - 1`

=> `1 + 1/(cos^2B) - 1`

=> `sec^2B`

This proves that: `(sec^2 B - 1)(cot^2 B + 1) = sec^2 B `

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