Question

Show that :

Cos2a = 1- 2sin^2a

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Answer 1

Here's your solution:

$\cos(2a) \\ \\ = \cos(a + a) \\ \\ = \cos(a) \cos(a) - \sin(a) \sin(a) \\ \\ = { \cos}^{2} a \: - { \sin }^{2} a \\ \\ = 1 - { \sin }^{2} a - { \sin }^{2} a \: (since \: \: {sin}^{2} a + {cos}^{2} a = 1) \\ \\ = 1 - 2 {sin}^{2} a$

Hence Shown

Answer 2

Answer is in attachment

Hope this will help ✌