Question

If cosecA is x+1/4x then prove that cosec +cot= 2x or 1/2x​

Answer 1

Given that,

cosec(A) = x + x/4 = 5x/4

So,

sin(A) = 4/5x ------------------- I

So, cos(A) = $\sqrt{1 - sin^{2}(A) }$

Hence, the simplified form,

$\sqrt{1 - 16/25x^{2} }$

$\sqrt{[25x^{2} - 16]/ 25x^{2} }$ ------------- II

Now, cosec(A) + cot(A) = 1/sin(A) + cos(A)/sin(A)

Which gives us,

[1 + cos(A)] / sin(A)

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Now, if you substitute the values in the equation, there is only square root answers. These are not simplified.

There may be a mistake in the question, a few of which I have found is:-

+> cosec(A) is x + 1/4x here there are a couple of mistakes. They could have given = instead of is , is it (1/4)x or just 1/4x.

+> cosec + cot does not exist, only cosec(A) and cot(A) exist.

Please correct the question.