1 + cot² α/(1 + cosec α) = cosec α. Prove the following statement

Solution:

LHS = 1 + cot² α/(1 + cosec α)

We know that

cot ² α = cosec² α - 1

So, LHS = 1 + (cosec² α - 1)/ (1 + cosec α)

Using the algebraic identity

a² - b² = (a + b) (a - b)

LHS = 1 + [(cosec α + 1) (cosec α - 1)/ (1 + cosec α)]

= 1 + cosec α - 1

= cosec α

= RHS

Therefore, it is proved.

✦ Try This: (tan² α - sin² α) cot² α/ sin² α = ___ a. 0, b. - 1, c. 1, d. None

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 6

1 + cot² α/(1 + cosec α) = cosec α. Prove the following statement

Summary:

The cosecant function is the ratio of the hypotenuse to the opposite side in a right angled triangle. It is proved that 1 + cot² α/(1 + cosec α) = cosec α

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