This ques has been taken from the Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter 18th
Chapter- Trigonometric Identities
This has been asked in previous year question
So it is very important ques
If 12 cosec θ = 13, find the value of (2 sin θ – 3 cos θ)/ (4 sin θ – 9 cos θ)
ML Aggarwal, ICSE, class10, chapter 18, question no 5
Given,
12 cosec θ = 13
⇒ cosec θ = 13/12
In right ∆ ABC,
∠A = θ
So, cosec θ = AC/BC = 13/12
AC = 13 and BC = 12
By Pythagoras theorem,
AB = √(AC2 – BC2)
= √[(13)2 – (12)2]
= √(169 – 144)
= √25
= 5
Now,
sin θ = BC/AC = 12/13
cos θ = AB/AC = 5/13
Hence,