Question

prove that root
$\sqrt{}$
1+cos A/1-cos A= cosec A+cot A​

Answer 1

Step-by-step explanation:

1−cosA

1+cosA

=

(1−cosA)(1+cosA)

(1+cosA)

2

=

sin

2

A

(1+cosA)

2

=

(cosecA+cotA)

2

=∣cosecA+cotA∣

=cosecA+cotA (as given)

let cosecA + cotA = x

so we get |x| = x

this is possible only when x ⩾ 0

so cosecA + cotA ⩾ 0

this means that sinA > 0

this is possible only in first and second quadrants

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