Question

proove that-1-2tanA(secA-tanA) =secA-tanA/secA+tanA​

Answer 1

Answer:

Step-by-step explanation:

Sec A - Tan A / Sec A + Tan A = 1 - (2 × Sec A × Tan A) + 2 Tan²A

_________________________________________________________

Identity to be used:

Sec²A = 1 + Tan²A

_________________________________________________________

Taking LHS,

= Sec A - Tan A / Sec A + Tan A  ×  Sec A - Tan A / Sec A - Tan A

= (Sec A - Tan A)² / (Sec A + Tan A)(Sec A - Tan A)

= (Sec A - Tan A)² / Sec²A - Tan²A

= Sec²A + Tan²A - 2 (Sec A × Tan A)

= 1 + Tan²A + Tan²A - 2 (Sec A × Tan A)

= 1 - 2 (Sec A × Tan A) + 2 Tan²A

______________________________________________________

☺☺☺ Hope this Helps ☺☺☺