Question

Find the value of Cos2A(1 + Tan2A)​

Answer 1

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Find the value of Cos2A(1 + Tan2A)

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${cos}^{2} a(1 + {tan}^{2} a)$

${cos}^{2} a( {sec}^{2} a - {tan}^{2} a + {tan}^{2} a)$

${cos}^{2} a( { \sec}^{2} a)$

${cos}^{2} a( \frac{1}{ {cos}^{2}a } )$

$1$

Identities Used :

• sec^2 a - tan^2 a = 1
• sec^2 a = 1 / cos^2 a

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Answer 2

Answer:

cos2a(1+tan2a)

{cos}^{2} a( {sec}^{2} a - {tan}^{2} a + {tan}^{2} a)cos2a(sec2a−tan2a+tan2a)

{cos}^{2} a( { \sec}^{2} a)cos2a(sec2a)

{cos}^{2} a( \frac{1}{ {cos}^{2}a } )cos2a(cos2a1)

11

Identities Used :

sec^2 a - tan^2 a = 1

sec^2 a = 1 / cos^2 a