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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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In a right-angled triangle, it is given that angle A is an acute angle and that
Tan A=5/12 Find the values of:
(i) cos A
(ii) cosec A- cot A.
Answer:
Here, ABC is the right-angled triangle
\angle \mathrm{A} \text { is an acute angle and } \angle \mathrm{C}=90^{\circ}
tan A = 5/12
BC/AC =5/12
Let BC = 5x and AC = 12x
From the right-angled ∆ABC
By Pythagoras theorem, we get
\begin{array}{l} A B^{2}=(5 x)^{2}+(12 x)^{2} \\ A B^{2}=25 x^{2}+144 x^{2} \\ A B^{2}=169 x^{2} \end{array}
(i) cos A = Base/ Hypotenuse
= AC / AB
= 12x/13x
=12/13
(ii) cosec A = Hypotenuse/perpendicular
= AC / BC
= 13x /5x
= 13/5
cot A = 13/5 – 12/5
= (13-12)/5
= 1/5
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