 # ML Aggarwal Solutions Class 9 Mathematics Solutions for Trigonometric Ratios Exercise 17 in Chapter 17 - Trigonometric Ratios

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.

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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