Question

Trig Question.

Answer 1

\[\frac{ cosec A }{ cosec A -1 } + \frac{ cosec A }{ cosec A +1 } = 2 \sec^2 A\]

Answer 2

its really straight forward...

you need a common denominator

\[(cosecA-1)(cosecA + 1) = ?\]

it's the difference of 2 squares...

then cross multiply in the numerator...

Answer 3

cosec^2 A -1?

Answer 4

great... are you sure the denominators are correctly written

Answer 5

Yes?

Answer 6

ok... so what do you get then you cross multiply in the numerator..?

Answer 7

cosecA(cosec A +1) and cosecA(cosecA-1)

Answer 8

great so that can simplfy to

Answer 9

?

Answer 10

How do I simplify it?

Answer 11

well \[cosecA(cosecA + 1) = cosec^2A + cosec A\]

and the do the same to the other term and what do you get...?

Answer 12

cosec^2 - cosec A

Answer 13

great so collect like terms in the numerator what do you get

\[cosec^2A + cosecA + cosec^2A - cosecA = ?\]

Answer 14

2 cosec^2 A

Answer 15

great so you problem is now

\[\frac{2cosec^2A}{cose^2A - 1}\]

does that make sense..?

Answer 16

the denominator is cot^2 right if i use the identity?

Answer 17

that's correct so in terms of sin and cos you have

\[\frac{2}{\sin^2A} \div \frac{\cos^2A}{\sin^2A}\]

now apply the rule for dividing by a fraction..

Answer 18

which is flip and multiply.... what do you get..?

Answer 19

2/cos^2 A

Answer 20

great so what do you know about

\[2 \times \frac{1}{\cos^2A}\]

it should be easy from here

Answer 21

2 sec^ A :)

Answer 22

great... nice and neat and simple... you knew what to do...

Answer 23

Thanks Sir.
Can you guide me through a few more questions?

Answer 24

well just post them... there are lots of people who can help