Question

prove that cosecA + cotA/cosecA - cotA = 1 + cot^2A + cosecAcotA

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:How do I show that (cosecA+cotA) (cosecA-cotA) = (1-cosecA+cotA)?

How do I show that (cosecA+cotA)(cosecA-cotA) = (1-cosecA+cotA)?

For this to be true, it must be true for all values of A

We’ll need the basic trigonometric identity: cos2(A)+sin2(A)=1

Dividing both sides of this identity by sin2(A), we get:

cot2(A)+1=cosec2(A) [Eq.1]

Now, let’s look at the left side of your equation.

[cosec(A)+cot(A)][cosec(A)−cot(A)]=cosec2(A)−cot2(A)

Using Eq.1, we can rewrite this as: cot2(A)+1−cot2(A)=1

So, your equation can be expressed as:

1=1−cosec(A)+cot(A)⇒cosec(A)=cot(A) [Eq.2]

Well, it certainly doesn’t look like your equation is true for all values of A! So, for what values of A is your equation true?

Well, lets multiply both sides of Eq.2 by sin(A)

We get 1=cos(A)⇒A=0∘+k180∘, where k is an integer

But we have a problem, for these values of A, cot(A) and cosec(A) are not defined!

So, not only is your equation not true for all values of A, it is never true!

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Ok now see u will be satisfied.

Thanks

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