sec² 54° - cot² 36° + \(\frac{3}{2}\) sin² 37° x sec² 53° + \(\frac{2}{\sqrt3}\) tan 60° এর মান কত?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 2)

Answer 1

ব্যবহৃত ধারণা :

tan(90° - θ) = cot θ

cot (90° - θ) = tan θ

sec (90° - θ) = cosec θ

cosec²θ - cot²θ = 1

sec²θ - tan²θ = 1

গণনা :

sec2 54° - cot2 36° + \(\frac{3}{2}\) sin2 37° × sec2 53° + \(\frac{2}{\sqrt3}\) tan 60°

⇒ sec2 54° - cot2 (90° - 54°) + \(\frac{3}{2}\) sin2 37° × sec2 (90° - 37°) + \(\frac{2}{\sqrt3}\) tan 60°

⇒ sec2 54° - tan2 54° + \(\frac{3}{2}\) sin2 37° × cosec2 37° + \(\frac{2}{\sqrt3}\) tan 60°

⇒ 1 + 3/2 + 2

⇒ 9/2

মানটি 9/2।

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