Question about ValuSoft Bible Collection (10281) for PC

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Hint: split it up into

int sec^2(x) dx + int e^sin(x) cos(x) dx

The first one is standard, and the second one is a straightforward u-substitution.

Posted on Jul 20, 2009

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Posted on Jan 02, 2017

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no idea what this ones all about

Sep 09, 2017 | Computers & Internet

( 2 tink 5 sec ) ) 3 set -lit extract )

Feb 02, 2012 | Health & Beauty

I going to use the following trig identies:

cotx = 1/tanx, and tanx = 1/cotx

Therefore:

(tanx+coty)/(tanx*coty) = (tanx + 1/tany)/(tanx/tany)

multiplying the top and bottom by tany yields:

(tany*tanx + 1) / tanx

This reduces to:

tany + 1/tanx

Which equals to:

tany + cotx

cotx = 1/tanx, and tanx = 1/cotx

Therefore:

(tanx+coty)/(tanx*coty) = (tanx + 1/tany)/(tanx/tany)

multiplying the top and bottom by tany yields:

(tany*tanx + 1) / tanx

This reduces to:

tany + 1/tanx

Which equals to:

tany + cotx

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I shall attempt :D

1) cosec A + cot A = 3

we know that (cot A)^2 + 1 = (cosec A)^2

Hence, (cosec A)^2 - (cot A)^2 = 1

thus, (cosec A + cot A) (cosec A - cot A) = 1

3 (cosec A - cot A) = 1

(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3

(cosec A + cot A) = 3

Summing them, 2 cosec A = 3 1/3

cosec A = 6 2/3 = 5/3

sin A = 0.15

Thus, cos A = sqrt (1 - (sin A)^2) = 0.989

2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2

expand

LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x

We can calculate that

tan x cosec x = sec x (since tan x = sin x / cos x)

sec x cot x = cosec x

so the above is

LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x

LHS = 2 + cot x + tan x - sec x cosec x

LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)

LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)

LHS = 2 (proved)

1) cosec A + cot A = 3

we know that (cot A)^2 + 1 = (cosec A)^2

Hence, (cosec A)^2 - (cot A)^2 = 1

thus, (cosec A + cot A) (cosec A - cot A) = 1

3 (cosec A - cot A) = 1

(cosec A - cot A) = 1/3

(cosec A - cot A) = 1/3

(cosec A + cot A) = 3

Summing them, 2 cosec A = 3 1/3

cosec A = 6 2/3 = 5/3

sin A = 0.15

Thus, cos A = sqrt (1 - (sin A)^2) = 0.989

2) Prove that (1+tan x - sec x)(1 + cot x + cosec x) =2

expand

LHS= 1 + cot x + cosec x + tan x + 1 + tan x cosec x - sec x - sec x cot x - sec x cosec x

We can calculate that

tan x cosec x = sec x (since tan x = sin x / cos x)

sec x cot x = cosec x

so the above is

LHS = 1 + cot x + cosec x + tan x + 1 + sec x - sec x - cosec x - sec x cosec x

LHS = 2 + cot x + tan x - sec x cosec x

LHS = 2 + cos x / sin x + sin x / cos x - 1 / (sin x cos x)

LHS = 2 + [{cos x}^2 + {sin x}^2 - 1] / (sin x cos x)

LHS = 2 (proved)

May 12, 2009 | ValuSoft Bible Collection (10281) for PC

tanx= sinx/cosx,

secx=1/cosx

1+sinx/cosx=3

1+sinx=3cosx---------->1

cosx=5-sinx------------->2

sub 2 in 1

1+sinx=3(5-sinx)

1+sinx=15-3sinx

1+4sinx=15

4sinx=14

sinx=14/4...

this is the solution..

secx=1/cosx

1+sinx/cosx=3

1+sinx=3cosx---------->1

cosx=5-sinx------------->2

sub 2 in 1

1+sinx=3(5-sinx)

1+sinx=15-3sinx

1+4sinx=15

4sinx=14

sinx=14/4...

this is the solution..

Jul 14, 2008 | ValuSoft Bible Collection (10281) for PC

Jan 23, 2009 | ValuSoft Bible Collection (10281) for PC

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