Question

prove the identity
√1+cos/1-cos = cosec + cot​

Answer 1

Answer:

Step-by-step explanation:

Explanation:

√

(

1

−

cos

θ

)

(

1

+

cos

θ

)

Recall: (1-costheta)(1+costheta) is an example of the difference of 2 squares. The general form is  

(

a

−

b

)

(

a

+

b

)

=

a

2

−

b

2

=  

√

1

−

cos

2

θ

Recall:  

sin

2

θ

+

cos

2

θ

=

1

so,  

1

−

cos

2

θ

=

sin

2

θ

=  

√

sin

2

θ

When you are square rooting a number, it can be positive or negative. Why?

Here's an example

2

2

=

4

and  

(

−

2

)

2

=

4

If you square a negative or positive number, its result will always be positive unless its a complex number.

=  

±

sin

θ

Answer 2

Step-by-step explanation:

First rationalise with underoot1+cos

In numerator and denominator

And on solving furthur we get the proof as shown in image

Thank you