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Trignometry

Blazing goIITian

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21 Aug 2007 20:56:51 IST

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469

sinA - tanA and secA + tanA are reciprocals.

None

my text book says

sinA - tanA and secA + tanA are reciprocals.

cosecA - cotA and cosecA + cotA are reciprocals.

but how?????

please explain

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Comments (11)

Nivedh Iyer

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21 Aug 2007 21:07:18 IST

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1st question shayad galat hai.............i may b wrong but plzz chk.........instead of sinA it should hav been secA................!!!!!!!!!!!!!

sinjan jana

Blazing goIITian

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21 Aug 2007 21:10:09 IST

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yeah

in this brilliant tutorial book it is given it may be wrong.

ok change the first question and then solve it..............!!!!!!!!!!!!!!!!1

sinjan jana

Blazing goIITian

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21 Aug 2007 21:10:38 IST

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do it now

Nivedh Iyer

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21 Aug 2007 21:11:43 IST

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answer2............
1/(cosecA-cotA) = sinA/(1-cosA).........

now,
cosecA+cotA = (1+cosA)/sinA = (1+cosA)(1-cosA)/sinA(1-cosA)
                                              = (1-cos^2A)/sinA(1-cosA)
                                              = sin^2A/sinA(1-cosA)
                                              =sinA/(1-cosA)............

therefore,

1/(cosecA-cotA) = sinA/(1-cosA) = cosecA+cotA..................!!!!!!!!!!!!!

Nivedh Iyer

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21 Aug 2007 21:15:02 IST

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answer1.....
similarly,
secA-tanA = (1-sinA)/cosA.................
1/(secA+tanA) = cosA/(1+sinA) = cosA(1-sinA)/(1-sin^2A) = (1-sinA)/cosA.........

So,

secA-tanA = 1/(secA+tanA)....................!!!!!!!!!!!!

sinjan jana

Blazing goIITian

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21 Aug 2007 21:16:04 IST

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thanx nivedh.............!!!!!!!!!!!

sinjan jana

Blazing goIITian

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21 Aug 2007 21:31:03 IST

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but nivedh i didnot understand this part

1/(secA+tanA) = cosA/(1+sinA)

Nivedh Iyer

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21 Aug 2007 21:32:33 IST

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1/(secA+tanA) = 1/(1/cosA+sinA/cosA) = 1/(1+sinA)/cosA = cosA/(1+sinA)......!!!!

santhosh in NUS

Hot goIITian

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21 Aug 2007 21:36:47 IST

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1. take conjugate

(secA-tanA) (secA+tanA)/(secA-tanA)

=sec²A-tan²A/secA-tanA

=1/secA-tanA (since sec²A-tan²A =1)

it is the same for next also.

i hope iam correct.rate me if it is

useful .

cheers!!!!!!!

sinjan jana

Blazing goIITian

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21 Aug 2007 21:43:06 IST

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123santoms explanation is very easy to understand....!!!!

well done....!!!!!

U ALREADY KNOW

Blazing goIITian

Joined: 16 Mar 2007

Posts: 838

21 Aug 2007 21:56:44 IST

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ya 123 santom and Nivedh have explained right Sinjan .

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