Math, asked by syedubada2, 1 year ago

secA-tanA/secA+tanA=1-2secA×tanA+2tanA

Answers

Answered by nitthesh7

Sec A - Tan A / Sec A + Tan A = 1 - (2 × Sec A × Tan A) + 2 Tan²A
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Identity to be used:

Sec²A = 1 + Tan²A
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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
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