Question

IF 13- 12 cosec A =0 find the of value 3 cos A-2tanA​

Answer 1

Step-by-step explanation:

Given,

12cosecθ=13,

⇒cosecθ=13/12,

In right ΔABC,

∠A=θ,

So, cosecθ=AC/BC=13/12

AC=13 and BC=12

By Pythagoras theorem,

AB=

(AC

2

−BC

2

)

=

((13)

2

−(12)

2

)

=

(169−144)

=

25

=5.

Now,

sinθ=BC/AC=12/13

cosθ=AB/AC=5/13.

Hence,

4sinθ−9cosθ

2sinθ−3cosθ

=

4∗

13

12

−9∗

13

5

2∗

13

12

−3∗

13

5

=

13

48

−

13

45

13

24

−

13

15

=

13

3

13

9

=

13

9

∗

3

13

=3.