Question

Express cos2A in terms of tanA

Answer 1

Step-by-step explanation:

cos 2A = cos2 A - sin2 A

cos 2A = cos2 A - sin2 Acos 2A = cos2A−sin2Acos2A ∙ cos2 A

cos 2A = cos2 A - sin2 Acos 2A = cos2A−sin2Acos2A ∙ cos2 A⇒ cos 2A = cos2 A (1 - tan2 A)

cos 2A = cos2 A - sin2 Acos 2A = cos2A−sin2Acos2A ∙ cos2 A⇒ cos 2A = cos2 A (1 - tan2 A)⇒ cos 2A = 1sec2A(1 - tan2 A)

cos 2A = cos2 A - sin2 Acos 2A = cos2A−sin2Acos2A ∙ cos2 A⇒ cos 2A = cos2 A (1 - tan2 A)⇒ cos 2A = 1sec2A(1 - tan2 A)⇒ cos 2A = 1−tan2A1+tan2A

Answer 2

Answer:

$\frac{1 -\tan ^ {2} a }{1 +\tan ^ {2} a }$

Step-by-step explanation:

As we know

Now multiplying by

${ \cos }^{2} a \:$

in the numerator and denominator

$= { \cos }^{2} a \: - { \sin}^{2} a \\ \times \frac{{ \cos }^{2} a}{{ \cos }^{2} a}$

$= \frac{(1 - { \ \tan }^{2} a)}{ \sec^{2} a }$

since,1/cos a = sec a

$1 + \tan^{2} a \: = \sec^{2} a$

$= \frac{1 - \tan^{2} a}{1 + \tan^{2} a}$

hope it helps