If 12 cosec θ = 13, find the value of (2 sin θ – 3 cos θ)/ (4 sin θ – 9 cos θ)

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deepaksoniGuru

Asked: March 15, 20212021-03-15T20:37:49+05:30 2021-03-15T20:37:49+05:30In: ICSE

This ques has been taken from the Book- ML Aggarwal
Board- ICSE
Publication- Avichal

Chapter 18th
Chapter- Trigonometric Identities

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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

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AAREKH · Answer 1 · 2021-03-15T21:22:33+05:30

AAREKH Guru

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,

ML Aggarwal Solutions for Class 10 Chapter 18 - 4