$(c o s e c A + s i n A) (c o s e c A - s i n A) = c o t^{2} A + c o s^{2} A$

Open in App

Solution

Taking L.H.S.
$(c o s e c A + s i n A) (c o s e c A - s i n A)$
$= c o s e c^{2} A - s i n^{2} A$
$= (1 + c o t^{2} A) - (1 - c o s^{2} A)$
$= c o t^{2} A + c o s^{2} A = R . H . S$

Suggest Corrections

Similar questions

\frac{cosec A - \sin A}{cosec A + \sin A} = \frac{\sec^{2} A - \tan^{2} A}{\sec^{2} A + \tan^{2} A}

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

c o s e c^{2} A = 1 + c o t^{2} 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

c o s e c^{2} A = 1 + c o t^{2} A

Prove that :

sinA / cotA + cosecA = 2 + sinA / cotA - cosecA

Join BYJU'S Learning Program