Question

secA (1-sinA)(secA+tanA)=1​

Answer 1

Step-by-step explanation:

=LHS= sec(1-sinA) (secA-tanA)

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

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

=(1-sin²A/cos²A)

Since, sin²A+cos²A=1

=cos²A=1-sin²A

therefore,

=(1-sin²A/cos²A)

=cos²A/cos²A=1

=1=RHS

=GOLDEN WORDS=HENCE, PROOVED

Answer 2

Step-by-step explanation:

L.H.S. = sec A ( 1 - sin A ) ( sec A + tan A)

= ( sec A - sec A.sinA) (sec A + tan A )

= (sec A - sin A/ cos A ) ( sec A + tan A)

= (sec A - tan A ) ( sec A - tan A)

= ( sec2 A - tan2 A)

= 1. R.H.S

Thanks