Question

Prove The Following.

$\large\frac{ \sin∅ \: - \: \cos∅ + 1 }{ \sin∅\cos∅=\frac{1}{ \sec∅ - \tan∅ }$
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Consider the L.H.S

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

Dividing in Nr and Dr by cosA.

=(tanA-1+secA)/(tanA+1-secA).

=(tanA+secA-1)/(tanA-secA+1).

putting 1= sec^2A-tan^2A=(secA-tanA).

(secA+tanA). in Dr.

=(tanA+secA-1)/{-(secA-tanA)+(secA-tanA).(secA+tanA)}.

=(tanA+secA-1)/(secA-tanA).(-1+secA+tanA).

= 1/(secA-tanA).

Hence Proved.