Show that 1sin A - cos A - 1 - 1sin A - cos A - 1 - sec A - cosec A

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

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Trigonometric Ratios

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Question

Show that $\frac{1}{s i n A + c o s A + 1} + \frac{1}{s i n A + c o s A - 1} = s e c A + c o s e c A$

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\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} = cos e c A + cot A

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

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