Q) Prove that: 1 + = cosec α (Q 22 B – 30/2/2 – CBSE 2026 Question Paper) Ans: Let’s start from LHS: LHS = 1 + Step 1: From Trigonometric identities, we know that 1 + cot 2 α = cosec 2 α ∴ cot 2 α = cosec 2 α – 1 Step 2: Let’s substitute the value of cot 2 […]

Prove that 1 + (cot^2 α)/(1 + cosec α) = cosec α

Q) Prove that: 1 + $\frac{(\cot^2 \alpha)}{(1 + \cos ec \alpha)}$ = cosec α

(Q 22 B – 30/2/2 – CBSE 2026 Question Paper)

Ans:

Let’s start from LHS:

LHS = 1 + $\frac{(\cot^2 \alpha)}{(1 + \cos ec \alpha)}$

Step 1: From Trigonometric identities, we know that

1 + cot ² α = cosec ² α

∴ cot ² α = cosec ² α – 1

Step 2: Let’s substitute the value of cot 2 α from stel 1:

LHS = 1 + $\frac{(\cot^2 \alpha)}{(1 + \cos ec \alpha)}$

= 1 + $\frac{(\cos ec^2 \alpha - 1)}{(1 + \cos ec \alpha)}$

= 1 + $\frac{(\cos ec \alpha - 1)(\cos ec \alpha + 1)}{(1 + \cos ec \alpha)}$

= 1 + $\frac{(\cos ec \alpha - 1)\cancel{(\cos ec \alpha + 1)}}{\cancel{(\cos ec \alpha + 1)}}$

= 1 + (cosec α – 1)

= cosec α = RHS

Hence Proved !

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