Question

Prove that 2 cos2 θ (1 + tan2 θ) = 2​

Answer 1

Step-by-step explanation:

LHS => 2 cos²A ( 1 + tan²A )

=> 2 cos²A ( 1 + sin²A/cos²A )

=> 2 cos²A [ ( cos²A + sin²A )/cos²A ]

=> 2 [ cos²A + sin²A ]

[ cos²A cancels out ]

=> 2 => RHS hence proved

[ identity used sin²A + cos²A = 1 ]