Prove that 1-cos Asin A -sin A1-cos A - 2cosec A-

L.H.S. 1+cos Asin A + sin A1+cos A = (1+cos A)^2 + sin^2 Asin A(1+cos A) = 1+cos^2 A + 2cos A + sin^2 A sin A (1+cos A) =2+2cos Asin (1+cos A ...

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Basic Trigonometric Identities

Prove that ...

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Prove that $\frac{1 + c o s A}{s i n A} + \frac{s i n A}{1 + c o s A} = 2 c o s e c A$ .

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\frac{sin A}{1 + cos A} + \frac{1 + cos A}{sin A} = 2 c o s e c A .

\frac{sin A}{1 + cos A} + \frac{1 + cos A}{sin A} = 2 cosec A

Prove the following trigonometric identities:

(i) $\sqrt{\frac{1 + s i n A}{1 - s i n A}} = s e c A + t a n A$

(ii) $\sqrt{\frac{1 - c o s A}{1 + c o s A}} + \sqrt{\frac{1 + c o s A}{1 - c o s A}} = 2 c o s e c A$

\frac{1 + cos A + sin A}{1 + cos A - sin A} = \frac{1 + sinA}{cos A}

\frac{sin A + cos A}{sin A - cos A} + \frac{sin A - cos A}{sin A + cos A} = \frac{2}{2 {sin}^{2} A - 1}

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