यदि sin2 θ = cos3 θ है, तो (cot2 θ - cot6 θ) का मान क्या है?

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SSC CPO 2022 Tier-I Official Paper (Held On 11 Nov 2022 Shift 2) [Answer Key]
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Option 1 : -1
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SSC CPO : English Comprehension Sectional Test 1
50 Qs. 50 Marks 20 Mins

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दिया है:

sin2 θ = cos3 θ

प्रयुक्त अवधारणा:

cosec2 θ – cot2 θ = 1

गणना:

⇒ प्रश्न के अनुसार, हमारे पास है 

 sin2 θ = cos3 θ

⇒  दोनों पक्षों का वर्ग करने पर 

⇒  sin4  θ = cos6  θ ....(1)

⇒ अब,

cot2 θ - cot6 θ = cot2 θ – 

⇒ समीकरण 1 से

cot2 θ –  = cot2 θ –  = cot2 θ – cosec2 θ = –1

इसलिए, cot2 θ - cot6 θ का मान – 1 है।

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