Help simplify (cos x / 1-sin x) + (1 - sinx / cosx)...?

Question

1. Enter 1.001 in your calculator and press the keys for inverse sine. explain why the response will indicate that something is wrong

2. y = cos^-1(sqrt3/2)
a) 63.61 degrees
b) 58.2 degrees
c) 27.79 degrees
d) 31.8 degrees

3. tan^-1 (.5774)
a) 32 degrees
b) 27 degrees
c) 60 degrees
d) 30 degrees

4. (cos x / 1-sin x) + (1 - sinx / cosx)
a) 2sec x
b) 2 csc X
c) sec^2 x
d) 2


please help best answer gets 10 points

TomV · Accepted Answer

Because 1.001 is outside the range of inverse sine. The range of the inverse sine is -1 to +1.

christopherthe1 · Answer

1. The range of the sine function is [-1,1].  This means that there is no argument for sine that will result in a number less than -1 nor greater than 1.  The inverse sine (arcsine) function, therefore, only exists in the same range.


2. The correct answer is not in the list of choices.  The arccosine (inverse cosine) for ((√3)/2) is 30°.  If that was meant to be √(3/2), then it's invalid because it's outside the domain of arccosine, which is also [-1,1].


3. d


4. (cos x / 1-sin x) + (1 - sinx / cosx)
= [(cos x)(1+sin x) / (1-sin x)(1+sin x)] + (1 - sinx / cosx)
= [(cos x)(1+sin x) / (1-sin²x)] + (1 - sinx / cosx)
= [(cos x)(1+sin x) / (cos²x)] + (1 - sinx / cosx)
= [(1+sin x) / (cos x)] + (1 - sinx / cosx)
= [(1+sin x) + (1-sin x)] / cosx
= 2/cos x
= 2sec x

Murtaza · Answer

(cos x / (1 - sin x ) ) + (1 - sin x)/cosx

cosx(1 + sin x) / (1 - sin²x )  + ( 1 - sin x)/cos x

cosx(1 + sinx )/cos²x  + (1 - sinx )/cosx

= 2/cosx = 2secx

The answer is a)

1.
Because , range of sine and cosine are from -1 to 1. 1.001 is greater than 1.

2 The answer is 30. Closest would be d)

3 The answer is d)

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Help simplify (cos x / 1-sin x) + (1 - sinx / cosx)...?

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