Question

1- Sin A ÷ 1+ Sin A = (Sec A- tan A) ²​

Answer 1

Step-by-step explanation:

L.H.S = 1 - sin A/ 1 + sin A.

Multiply both the numerator and denominator by ( 1 - sin A)

= (1 - sin A) / (1 + sin A) × (1 - sin A) / 1 - sin A).

= (1 - sin A)^2 / 1 - sin^ 2 A.

so, from { sin^2 A + cos ^ 2 A=1}

= (1 - sin A)^ 2/ cos^2 A.

= 1 + sin^ 2 A - 2 sin A / cos^2 A.

= sec^ 2 A + tan^2 A - 2 sec A × tan A.

= (sec A - tan A)^ 2.

L.H.S = R.H.S

Proved

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