Krishna
0

Step 1: Consider a right angle triangle

NOTE: Right angle triangle ABC with right angle is at B

Step 2: Write the Pythagoras theorem to the triangle.

NOTE: Take the angle A

(hypotenuse)^2 = (opposite)^2 + (adjacent)^2

AC^2 = BC^2 + AB^2

Step 3: Dividing each term by opposite side.(BC) and simplify

EXAMPLE: \frac{AC^2}{BC^2} = \frac{AB^2}{BC^2} + \frac{BC^2}{BC^2}

(\frac{AC}{BC})^2 = (\frac{AB}{BC})^2 + (\frac{BC}{BC})^2

(\frac{hypotenuse}{opposite})^2 = (\frac{adjacent}{opposite})^2 + 1^2

(\cosec A)^2 = (\cot A)^2 + 1

1 + \cot^2 A = \cosec^2 A