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ML Aggarwal Solutions Class 9 Mathematics Solutions for Trigonometric Ratios Exercise 17 in Chapter 17 - Trigonometric Ratios
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If cosec = √5 and is less than 90, find the value of cot - Cos
Answer:
Given cosec θ = √5/1 = OP/PM
OP = √5 and PM = 1
Now \mathrm{OP}^{2}=\mathrm{OM}^{2}+\mathrm{PM}^{2} using Pythagoras theorem
\begin{array}{l} (\sqrt{5})^{2}=O M^{2}+1^{2} \\ 5=O M^{2}+1 \\ O M^{2}=5-1 \\ O M^{2}=4 \\ O M=2 \end{array}
Now cot θ = OM/PM
= 2/1
= 2
Cos θ = OM/OP
= 2/√5
Now cot θ - Cos θ = 2 – (2/√5)
= 2 (√5 – 1)/ 2/√5
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