Question

If θ is an acute angle and cosecθ = √5 , find the value of cotθ− cosθ​

Answer 1

Answer:

Given,

θ is an acute angle and cosecθ=

5

,

So,

sinθ=1/

5

And, cosθ=

(1−sin

2

θ)

cosθ=

(1−(1/

5

)

2

)

=

(1−(1/5))

=

(4/5)

cosθ=2/

5

Now,

cotθ−cosθ=(cosθ/sinθ)−cosθ

=

1−(

5

1

)

2

=

1−

5

1

=

5

5−1

=

5

4

=

5

2

.