Prove that - cos A - sin A - 1-cos A - sin A - 1 - cos ecA - A

LHS =cos A sin A+1cos A+sin A 1 =sin A(cos A sin A+1)sin (cos A+sin A 1) =cos Asin A sin^2A+sin Acos Asin A+sin^2A sin A =sin Acos A+sin A ( ...

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Trigonometric Ratios of Common Angles

Prove that : ...

Question

Prove that : $\frac{cos A - sin A + 1}{cos A + sin A - 1} = cos e c A + cot A$

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\frac{c o s A - s i n A + 1}{c o s A + s i n A - 1} = \frac{1}{c o s e c A - c o t A}

\frac{c o s A - s i n A + 1}{c o s A + s i n A - 1} = c o s e c A + c o t A

\frac{cos A - sin A + 1}{cos A + sin A - 1} = c o s e c A + cot A

\frac{c o t A + c o s e c A - 1}{c o t A - c o s e c A + 1} = \frac{1 + c o s A}{s i n A} = c o s e c θ + c o t θ = \frac{s i n A}{1 - c o s A}

\frac{cos A + sin A - 1}{cos A - sin A + 1} = \frac{1}{cosec A + cot A}

{cosec}^{2} A - {cot}^{2} A = 1.

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