Question
Download Solution PDFIf sin θ = 2/√5, find the value of sec2θ + cot2θ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sinθ = 2/√5
Concept:
Using the trigonometric function, calculate the values of sec θ and cot θ.
Calculation:
sin θ = (Perpendicular)/(Hypotenuse)
In ∆ABC;
(AC)2 = (AB)2 + (BC)2
⇒ (√5)2 = (2)2 + (BC)2
⇒ 5 = 4 + (BC)2
⇒ (BC)2 = 5 – 4
⇒ (BC)2 = 1
⇒ BC = 1
sec θ = (Hypotenuse)/Base)
⇒ sec θ = √5/1 = √5
cot θ = (Base)/(perpendicular)
⇒ cot θ = 1/2
(sec θ)2 + (cot θ)2 = (√5)2 + (1/2)2
⇒ 5 + 1/4
⇒ 21/4
∴ The value of sec2θ + cot2θ is 21/4.
Last updated on Jul 21, 2025
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