Question

cos theta +sin theta /sin theta=1+cot theta​

Answer 1

Step-by-step explanation:

ANSWER:-

TO PROVE:-

$\frac{ \cos\theta + \sin\theta }{\sin\theta} = 1 + cot \theta$

PROOF:-

We know that

$cot \theta = \frac{cos \theta}{sin\theta}$

So, dividing the whole equation by sin theta, we get:-

$\frac{ \frac{cos\theta + sin\theta}{sin\theta} }{ \frac{sin\theta}{sin\theta} }$

Solving in Numerator,

$\frac{cos\theta}{sin\theta} + \frac{sin\theta}{sin\theta}$

$= cot\theta + 1$

Now in Denominator,

$\frac{sin\theta}{sin\theta} = 1$

So,

LHS = Cot theta +1

RHS = Cot theta + 1

Hence Proved.

Answer 2

Extra knowledge

Sine Function:

• sin(θ) = Opposite / Hypotenuse

Cosine Function:

• cos(θ) = Adjacent / Hypotenuse

Tangent Function:

• tan(θ) = Opposite / Adjacent.

Sine Function:

• sin(θ) = Opposite / Hypotenuse

Cosine Function:

• cos(θ) = Adjacent / Hypotenuse

Tangent Function:

• tan(θ) = Opposite / Adjacent

For a given angle θ each ratio stays the same no matter how big or small the triangle is