Question

Trigonometry

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Answer 1

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Answer 2

Answer:

(secA − tanA) / (secA + tanA) 

= (1/cosA − sinA/cosA) / (1/cosA + sinA/cosA) 

= (1 − sinA) / (1 + sinA) 

= {(1 − sinA)(1 − sinA)} / {(1 + sinA)(1 − sinA)}

= (1 − 2sinA + sin²A) / (1 − sin²A) 

= (cos²A + sin²A − 2sinA + sin²A) / cos²A 

= (cos²A − 2sinA + 2sin²A) / cos²A 

= cos²A/cos²A − 2 (1/cosA)( sinA/cosA) + 2(sin²A/cos²A )

= 1 − 2secAtanA + 2tan²A

= RHS