Question
Download Solution PDFWhat is the value of sec2 54° - cot2 36° + \(\frac{3}{2}\) sin2 37° × sec2 53° + \(\frac{2}{\sqrt3}\) tan 60°?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used :
tan(90° - θ) = cot θ
cot (90° - θ) = tan θ
sec (90° - θ) = cosec θ
cosec2θ - cot2θ = 1
sec2θ - tan2θ = 1
Calculations :
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
The value is 9/2.
Last updated on Jul 19, 2025
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