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Trigonometry

Multiple Choice Questions

101.

If θ is positive acute angle and 4 sin²θ = 3, then the value of $tan space straight theta space minus space cot space straight theta over 2$ is

1
0
$square root of 3$
$fraction numerator 1 over denominator square root of 3 end fraction$

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102.

If $straight r space sin space straight theta space equals space 7 over 2$ and $straight r space cos space straight theta space equals space fraction numerator 7 square root of 3 over denominator 2 end fraction$ then the value of θ is

30°
45°
60°
75°

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103.

If $tan space straight theta space equals space 1 comma$ then the value of $fraction numerator 8 space sin space straight theta space plus space 5 space cos space straight theta over denominator sin cubed straight theta space minus space 2 cos cubed straight theta space plus space 7 cosθ end fraction$ is

1
3
2
$1 half$

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104.

If $sin space 31 degree space equals space straight x over straight y$ , the value of $sec space 31 degree space minus space sin space 59 degree$ is

$fraction numerator straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction$
$negative fraction numerator straight x squared over denominator straight y square root of straight y squared minus straight x squared end root end fraction$
$negative fraction numerator straight y squared over denominator square root of straight y squared minus straight x squared end root end fraction$
$negative fraction numerator straight x squared over denominator square root of straight y squared minus straight x squared end root end fraction$

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105.

If sinA + sin²A = 1, what is the value of cos² + cos⁴A = ?

$1 half$
1
2
3

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106.

ABC is a right angled triangle with $angle straight A space equals space 90 degree.$ Then the value of cos²A + cos²B + cos²C is:

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107.

The value of cosec²60° + sec²60° - cot²60° + tan²30° will be

5
$5 1 half$
$5 1 third$
$5 2 over 3$

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108.

If sin θ + cosec θ = 2, the value of sinⁿθ + cosecⁿθ is

2n
$2 to the power of 1 over straight n end exponent$
2
0

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109.

The value of $sec squared 17 degree space minus space fraction numerator 1 over denominator tan squared 73 degree end fraction space minus space sin space 17 degree space space sec space 73 degree$ is

1
0
-1
2

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110.
If $straight x space equals space straight a space cos space straight theta space cosÏ• comma space space space straight y space equals space straight a space cos space straight theta space sin space straight Ï• space space space and space space straight z space equals space straight a space sin space straight theta comma$ then the value of x² + y² + z² is

2a²

4a²

9a²

a²

a²

$straight x space equals space straight a space cos space straight theta space cos space straight Ï• space space space space space... left parenthesis straight i right parenthesis straight y space equals space straight a space cos space straight theta space sin space straight Ï• space space space space space space... left parenthesis ii right parenthesis straight z space equals space straight a space sin space straight theta space space space space space space space space space space space space space space... left parenthesis iii right parenthesis$
Squaring and adding (i), (ii), (iii)
$straight x squared space plus space straight y squared space plus space straight z squared space equals space left parenthesis straight a space cos space straight theta space cos space straight Ï• right parenthesis squared space plus space left parenthesis straight a space cos space straight theta space sin space straight Ï• right parenthesis squared space plus space left parenthesis straight a space sin space straight theta right parenthesis squared space equals space straight a squared space cos squared straight theta space cos squared straight Ï• space plus space straight a squared cos squared straight theta space sin squared straight Ï• space plus space straight a squared sin squared straight theta equals space straight a squared left square bracket cos squared straight theta space cos squared straight Ï• space plus space cos squared straight theta space sin squared straight Ï• space plus space sin squared straight theta right square bracket equals space straight a squared open square brackets cos squared straight theta space left parenthesis cos squared straight Ï• space plus space sin squared straight Ï• right parenthesis space plus space sin squared straight theta close square brackets equals space straight a squared left square bracket cos squared straight theta space plus space sin squared straight theta right square bracket equals space straight a squared$

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Multiple Choice Questions

110. If then the value of x2 + y2 + z2 is 2a2 4a2 9a2 a2