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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

$1 half$

tan θ = 1
tan θ = tan 45°
θ = 45°
Now,
$fraction numerator 8 space sin space straight theta space plus space 5 space cos space straight theta over denominator sin cubed straight theta space minus space 2 space cos cubed straight theta space plus space 7 space cos space straight theta end fraction space equals space fraction numerator 8 space sin space 45 degree space plus 5 space cos space 45 degree over denominator sin cubed 45 degree space minus 2 cos cubed 45 degree space plus space 7 space cos space 45 degree end fraction$
$equals space fraction numerator begin display style fraction numerator 8 over denominator square root of 2 end fraction end style space plus space begin display style fraction numerator 5 over denominator square root of 2 end fraction end style over denominator open parentheses begin display style fraction numerator 1 over denominator square root of 2 end fraction end style close parentheses cubed space minus space 2 open parentheses begin display style fraction numerator 1 over denominator square root of 2 end fraction end style close parentheses cubed space plus space begin display style fraction numerator 7 over denominator square root of 2 end fraction end style end fraction equals space fraction numerator begin display style fraction numerator 13 over denominator square root of 2 end fraction end style over denominator begin display style fraction numerator 1 over denominator 2 square root of 12 end fraction end style minus 2 cross times begin display style fraction numerator 1 over denominator 2 square root of 2 end fraction end style space plus space begin display style fraction numerator 7 over denominator square root of 2 end fraction end style end fraction equals space fraction numerator begin display style fraction numerator 13 over denominator square root of 2 end fraction end style over denominator begin display style fraction numerator 1 minus 2 plus 14 over denominator 2 square root of 2 end fraction end style end fraction space equals space fraction numerator 13 over denominator square root of 2 end fraction space cross times space fraction numerator 2 square root of 2 over denominator 13 end fraction space equals space 2$

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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:

47 Views

107.

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

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

90 Views

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

65 Views

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

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Previous Year Papers

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Multiple Choice Questions

103. If then the value of is 1 3 2