Question

Prove that: sec (1 − sin )(sec + tan) = 1.

Answer 1

Answer:

LHS = sec(1-sin)(sec+tan)

= sec (1-sin)(1/cos+sin/cos)

= sec (1-sin)(1+sin/cos)

= sec (1-sin²/cos)

= sec(cos²/cos)

= sec × cos

= 1/cos × cos

= 1

= RHS

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