Question

1
13. Prove that 1/sinA-sinA=cotA.cosA​

Answer 1

Step-by-step explanation:

1/SinA-SinA

1-Sin^2A/SinA

cos^2A/SinA

CosA×CosA/SinA

CosA/SinA×CosA

CotA.CosA

Hope it helps you!

Answer 2

Given:

1/sinA-sinA

To prove:

1/sinA-sinA=cotA.cosA​

Proof:

We can start by simplifying the left-hand side of the equation using the difference of squares formula:

1/sinA - sinA = (1 - sin^2 A)/sinA

Next, we can use the Pythagorean identity to substitute sin^2 A with 1 - cos^2 A:

(1 - sin^2 A)/sinA = cos^2 A / sinA

Now we can simplify the right-hand side of the equation by using the definition of cotangent and cosine:

cotA.cosA = cosA/sinA

Since cos^2 A/sinA = cosA/sinA, we have proven that:

1/sinA - sinA = cotA.cosA


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