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Conditional Identities

2A cosec2 B-2...

Question

${cot}^{2} A {cosec}^{2} B - {cot}^{2} B {cosec}^{2} A = {cot}^{2} A - {cot}^{2} B$

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Solution

Simplifying the LHS of ${cot}^{2} A {csc}^{2} B - {cot}^{2} B {csc}^{2} A = {cot}^{2} A - {cot}^{2} B$ .

${cot}^{2} A {csc}^{2} B - {cot}^{2} B {csc}^{2} A = {cot}^{2} A (1 + {cot}^{2} B) - {cot}^{2} B (1 + {cot}^{2} A)$

$= {cot}^{2} A + {cot}^{2} A {cot}^{2} B - {cot}^{2} B - {cot}^{2} A {cot}^{2} B$

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

$= R H S$

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Similar questions

Q. Prove the following trigonometric identities.

cot² A cosec² B − cot² B cosec² A = cot² A − cot² B

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

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

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

Q. Question 32

The value of

(a + b)^{2} + (a - b)^{2}

2 a + 2 b

2 a - 2 b

2 a^{2} + 2 b^{2}

2 a^{2} + 2 b^{2}

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