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Trigonometric Ratio(sin,cos,tan)

Prove that Co...

Question

Prove that

Cot²A × cosec²A - cot²B × cosec² B = cot²A - cot² B

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Solution

cot^2A cosec^2B - cot^2B cosec^2A
= cot^2A (1 + cot^2B) - cot^2B (1 + cot^2A)
= cot^2A + cot^2Acot^2B - cot^2B - cot^2Bcot^2A
= cot^2A - cot^2B

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c o t^{2} A c o s e c^{2} B - c o t^{2} B c o s e c^{2} A = c o s e c^{2} A - c o s e c^{2} B

{tan}^{2} A {sec}^{2} B - {sec}^{2} A {tan}^{2} B = {tan}^{2} A - {tan}^{2} B

{sin}^{2} A {cos}^{2} B - {cos}^{2} A {sin}^{2} B = {sin}^{2} A - {sin}^{2} B

Q. Prove that :

{sec}^{2} A + cosec^{2} A = {sec}^{2} A \times cosec^{2} A

{cot}^{2} A {csc}^{2} B - {cot}^{2} B {csc}^{2} A = {cot}^{2} A - {cot}^{2} B

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