Question

prove that sec(1-sin)×(sec+tan)= 1​

Answer 1

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$( \sec(1 - \sin )) ( \sec + \tan) \\ ( \sec - \sec \sin) ( \sec + \tan) \\ ( \sec - \tan)( \sec + \tan ) \\ { \sec }^{2} - { \tan }^{2} \\ 1$

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Answer 2

Answer:

sec(1-sin)×(sec+tan)=1

L.H.S,

sec(1-sin)×(1/cos+sin/cos)

sec(1-sin)×[(1+sin)/cos]

sec(1-sin²)/cos --- [(1-sin²)=cos²]

sec(cos²/cos)=sec×cos=(1/cos)×cos=1=R.H.S

proved.

Step-by-step explanation: