Q. 24.4( 159 Votes )

If cosec

Answer :

**Given:**

[∵, tan θ = cot (90° - θ)]

= 1

**OR**

**Given:** cosec^{2} θ (1 + cos θ) (1 – cos θ) = k

To find: Value of k

Proof: Taking LHS

= cosec^{2} θ (1 + cos θ) (1 – cos θ)

Using the identity,

**(a + b)(a – b) = (a ^{2} – b^{2})**

= cosec^{2} θ [(1)^{2} – (cosθ)^{2}]

= cosec^{2} θ [ 1 – cos^{2}θ] …(i)

We know that,

**cos ^{2}θ + sin^{2}θ = 1**

**or sin ^{2}θ = 1 – cos^{2}θ**

So, equation (i) becomes,

= cosec^{2}θ (sin^{2}θ) …(ii)

Now, we also know that,

So, equation (ii) becomes

= 1

∴ cosec^{2} θ (1 + cos θ) (1 – cos θ) = 1 = k

Hence, the value of k is 1

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