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If A+B=45^{o}, prove that ( A-1)( B-1)=2

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If $A + B = 4 5^{o}$ , prove that $(cot A - 1) (cot B - 1) = 2$

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A + B = 4 5^{o}

, prove that

(cot A - 1) (cot B - 1) = 2

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Text solutionVerified

Given

A + B = 4 5^{\circ}

⟹ cot (A + B) = cot 4 5^{\circ}

⟹ \frac{cot A cot B - 1}{cot A + cot B} = 1

⟹ cot A cot B - 1 = cot A + cot B

⟹ cot A cot B - cot A - cot B = 1

⟹ cot A cot B - cot A - cot B + 1 = 2

⟹ cot A (cot B - 1) - (cot B - 1) = 2

⟹ (cot A - 1) (cot B - 1) = 2

Hence proved.

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