যদি \(tan^2\theta + tan^4\theta = 1\), তাহলে:

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Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 3)

Answer 1

প্রদত্ত :

tan² θ + tan⁴ θ = 1

অনুসৃত ধারণা :

tan2 θ + 1 = sec² θ

গণনা :

⇒ tan2 θ + tan4 θ = 1

⇒ tan2 θ (1 + tan2 θ) = 1

⇒ tan2 θ × sec² θ = 1

⇒ tan2 θ = 1/sec² θ = cos² θ

এখন সমীকরণে tan2 θ এর মান রেখে পাই :

⇒ tan2 θ + tan4 θ = 1

⇒ tan2 θ + (tan²)² θ = 1

⇒ cos2 θ + (cos²)² θ = 1

⇒ cos² θ + cos⁴ θ = 1

∴ সঠিক বিকল্প হল 2

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