Question

If cot 0-2
evalulate 3 cos o #2sin o
4cos o - Sino
3​

Answer 1

Step-by-step explanation:

10th

Maths

Introduction to Trigonometry

Trigonometric Ratios

If 3sinθ + 4cosθ = 5 , the...

MATHS

If 3sinθ+4cosθ=5, then find cotθ+cosecθ

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ANSWER

Given, 3sinθ+4cosθ=5

3sinθ=5−4cosθ, squaring we get:

9sin

2

θ=25+16cos

2

θ−40cosθ

9(1−cos

2

θ)=25+16cos

2

θ−40cosθ(∵sin

2

θ=1−cos

2

θ)

9−9cos

2

θ=25+16cos

2

θ−40cosθ

⇒16cos

2

θ+9cos

2

θ−40cosθ+25−9=0

⇒25cos

2

θ−40cosθ+16=0

⇒(5cosθ−4)

2

=0

⇒5cosθ−4=0

⇒5cosθ=4

⇒cosθ=

5

4

cosecθ=

P

H

=

PQ

OP

=

3

5

cotθ=

P

B

=

PQ

OQ

=

3

4

Required Expression =cosecθ+cotθ

=

3

5

+

3

4

=

3

4

=

3

9

=3

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