Question

prove that secA-tanA=1​

Answer 1

Answer:

sec²A-tan²A=1​

Step-by-step explanation:

Prove that sec²A-tan²A=1​

LHS = sec²A-tan²A

RHS = 1

Lets solve LHS

LHS

= sec²A-tan²A

SecA = 1/CosA

=> sec²A = 1/Cos²A

Tan A = SinA/CosA

=> Tan²A = Sin²A/Cos²A

putting these values

LHS

= 1/Cos²A - Sin²A/Cos²A

= (1 -Sin²A)/Cos²A

Sin²A + Cos²A = 1 => 1 -Sin²A = Cos²A

=   Cos²A/Cos²A

= 1

= RHS

QED

Proved