Question

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Answer 1

Answer:

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Answer 2

Answer:

Refer to the "Step-by-step explanation"...

Step-by-step explanation:

$LHS\\\\\\= \dfrac{cos \theta}{1 + sin\theta} + \dfrac{1 + sin \theta}{cos \theta}\\\\\\= \dfrac{cos^2 \theta + (1 + sin \theta)^2}{(1+sin \theta)cos \theta}\\\\\\= \dfrac{cos^2 \theta + 1^2 + sin^2 \theta + 2(1)sin \theta}{(1+sin \theta)cos \\\theta}\\\\\\= \dfrac{sin^2 \theta + cos^2 \theta + 1 + 2sin\theta}{(1 + sin \theta)cos \theta}\\\\\\= \dfrac{1 + 1 + 2sin\theta}{(1 + sin\theta)cos\theta}\\\\\\= \dfrac{2 + 2sin\theta}{(1 + sin\theta)cos\theta}$

$= \dfrac{2(1 + sin\theta)}{(1 + sin\theta)cos\theta}\\\\\\= \dfrac{2}{cos\theta}\\\\\\= 2 cos\theta\\\\\\= RHS$

LHS = RHS

Hence Proved

Identities Used:

1. sin²Ф + cos²Ф = 1
2. 1/cosФ = secФ
3. (a+b)² = a² + b² + 2ab