# If Cot Theta = 1/Sqrt3 Show That (1 - Cos^2 Theta)/(2 - Sin^2 Theta) = 3/5 - Mathematics

#### Question

If cot theta = 1/sqrt3 show that  (1 - cos^2 theta)/(2 - sin^2  theta) = 3/5

#### Solution

cot theta = 1/sqrt3 (1 - cos^2 theta)/(2 - sin^2 theta) = 3/5

cot theta = "𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒"/"𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒" = 1/sqrt3

Let x be the hypotenuse

By applying Pythagoras

𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2

x^2 = (sqrt3)^2 + 1

x^2 = 3 + 1

𝑥2 = 3 + 1 ⇒ 𝑥 = 2

cos theta = (BC)/(AC) = 1/2

sin theta = (AB)/(AC) = sqrt3/2

(1 - cos^2 theta)/(2 - sin^2 theta) => (1 - (1/2)^2)/(2 - (sqrt3)/2)^2

=> (1 - 1/4)/(2 - 3/4) => (3/4)/(5/4

= 3/5

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Exercise 10.1 | Q 15 | Page 24
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 10: Trigonometric Ratios
Exercise 10.1 | Q 15 | Page 24
If Cot Theta = 1/Sqrt3 Show That (1 - Cos^2 Theta)/(2 - Sin^2 Theta) = 3/5 Concept: Trigonometric Ratios.