Question

Hello!!


Question :


Prove that, (cosec∅-cot∅)² = (1-cos∅)/(1+cos∅)

Answer 1

$\huge\underline\mathfrak\red{Question}$

Prove that :

(cosec∅-cot∅)² = (1-cos∅)/(1+cos∅)

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$\huge\underline\mathfrak\red{Explanation}$

LHS :

(cosec∅ - cot∅)² .....(i)

we know that,

cosec∅ = 1/sin∅

cot∅ = cos∅/sin∅

Now put the above values in (i)

we get,

[1/sin∅ - (cos∅/sin∅)]²

Taking sin∅ as LCM,

We get,

[(1 - cos∅)/sin∅]²

=> (1-cos∅)²/sin²∅ .......[A]

RHS :

(1-cos∅)/(1+cos∅)

After rationalising,

(1-cos∅)/(1+cos∅) × (1-cos∅)/(1-cos∅)

=> (1-cos∅)²/[(1)² - (cos∅)²]

=> (1-cos∅)²/(1-cos²∅)....(ii)

Now, we also know that,

sin²∅ + cos²∅ = 1

So, sin²∅ = 1 - cos²∅

put this value in (ii),

=> (1-cos∅)²/sin²∅ ......[B]

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From [A] and [B],

LHS = RHS

Hence proved!

Answer 2

hey mate please refer to the attachment

there is two methods ,,,short and long ,,u can see .