Question

SecA(1-sinA) (secA+tanA)=1

Answer 1

secA (1-sinA) (secA + tan A) 

= (secA-sinA×secA)(secA+tanA)

=(secA-tanA) (secA+tanA)  as secA=1/cosA and sinA/cosA=tanA

= (sec²A-tan²A) as (a+b)(a-b)=a²-b²

=sec²A-tan²A=1 from identity.

Hence proved.

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Answer 2

Step-by-step explanation:

LHS

secA is 1/cos

1/cos(1-sinA)

=1/cos-sinA/cosA

=(secA-tanA)(secA+tanA)

=Sec^2A-tan^2A=

because tan^2A+1=sec^2A

=1=sec^2A-tan^2

therefore

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