If 2tan x + 3cot x = 5, then the value o

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Trigonometry

Question:

If 2tan x + 3cot x = 5, then the value of $4tan^2 x + 9cot^2 x$ is :

Options:

Correct Answer:

Explanation:

2tan x + 3cot x = 5

Let x = 45º

2tan 45º + 3cot 45º = 5

{ we know, tan 45º = 1 }

2 × 1 + 3× 1 = 5

5 = 5 ( satisfied )

Now,

4 tan²x + 9 tan²x

= 4 tan²45º + 9 tan²45º

= 4 × 1 + 9 × 1

= 13