Question

Sin a - Cos A+1 divided by
Sin A+ CosA-1=
Sec A+ tan A​

Answer 1

Answer:

LHS

\frac{\sin A-\cos A+1}{\sin A+\cos A-1}sinA+cosA−1sinA−cosA+1

Divide numerator  and denominator by cos A

\frac{\frac{sinA}{cosA}-\frac{cosA}{cosA}+\frac{1}{cos A}}{\frac{sinA}{cosA}+\frac{cosA}{cosA}-\frac{1}{cos A}}cosAsinA+cosAcosA−cosA1cosAsinA−cosAcosA+cosA1

\frac{tanA-1+secA}{tanA+1-secA}tanA+1−secAtanA−1+secA

Using the formula

tan A=\frac{sinA}{cos A}tanA=cosAsinA

sec A=\frac{1}{cos A}secA=cosA1

\frac{tanA+secA-1}{tanA-secA+sec^2A-tan^2 A}tanA−secA+sec2A−tan2AtanA+secA−1

Using the formula

sec^2 A-tan^2A=1sec2A−tan2A=1

\frac{tanA+secA-1}{tanA-secA+(secA-tanA)(secA+tanA)}tanA−secA+(secA−tanA)(secA+tanA)tanA+secA−1

\frac{tanA+secA-1}{secA-tanA(-1+secA+tanA)}secA−tanA(−1+secA+tanA)tanA+secA−1

\frac{1}{secA-tanA}secA−tanA1

LHS=RHS