Prove nbsp-that nbsp- cot A cosec2 nbsp-B - cosec2 nbsp-A cot2 nbsp-B - cot nbsp-2 A - cot2 B

Dear Student, Assuming question is LHScot2A #160;cosec2B cosec2A #160;cot2B=cot2A #160;1+cot2B 1+cot2Acot2B=cot2A+cot2A #160;cot2B cot2B cot2A #160;c ...

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Standard X

Mathematics

Trigonometric Ratio(sin,cos,tan)

Prove nbsp...

Question

Prove that : cot A cosec²B - cosec²A cot²B = cot ² A - cot² B

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Solution

Dear Student,

Assuming question is
$LHS \cot^{2} A {cosec}^{2} B - {cosec}^{2} A \cot^{2} B = \cot^{2} A (1 + \cot^{2} B) - (1 + \cot^{2} A) \cot^{2} B = \cot^{2} A + \cot^{2} A \cot^{2} B - \cot^{2} B - \cot^{2} A \cot^{2} B = \cot^{2} A - \cot^{2} B = RHS Hence Proved$

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Prove that : cot A cosec2 B - cosec2 A cot2 B = cot 2 A - cot2 B

Dear Student, Assuming question is LHScot2A cosec2B-cosec2A cot2B=cot2A 1+cot2B-1+cot2Acot2B=cot2A+cot2A cot2B-cot2B-cot2A cot2B=cot2A-cot2B=RHSHence Proved

Prove that : cot A cosec²B - cosec²A cot²B = cot ² A - cot² B

Dear Student,

Assuming question is
$LHS \cot^{2} A {cosec}^{2} B - {cosec}^{2} A \cot^{2} B = \cot^{2} A (1 + \cot^{2} B) - (1 + \cot^{2} A) \cot^{2} B = \cot^{2} A + \cot^{2} A \cot^{2} B - \cot^{2} B - \cot^{2} A \cot^{2} B = \cot^{2} A - \cot^{2} B = RHS Hence Proved$