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Trigonometry

Multiple Choice Questions

131.

If $straight P space sin space straight theta space equals space square root of 3$ and P cosθ = 1, then the value of P is

$fraction numerator 2 over denominator square root of 3 end fraction$
$negative fraction numerator 1 over denominator square root of 3 end fraction$
2
$1 half$

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132.

The value of $fraction numerator 1 over denominator left parenthesis 1 plus tan squared straight theta right parenthesis end fraction space plus space fraction numerator 1 over denominator left parenthesis 1 plus cot squared straight theta right parenthesis end fraction$ is

1
2
$1 half$
$1 fourth$

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133.

If $tan space straight theta space equals space 3 over 4$ and θ is acute, then cosec θ is equal to

$5 over 3$
$5 over 4$
$4 over 3$
$4 over 5$

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134.
If $cos space straight theta space plus space sin space straight theta space equals space square root of 2 space cos space straight theta comma$ then cos θ - sin θ is

$negative square root of 2 space cos space straight theta$

$negative square root of 2 space sin space straight theta$

$square root of 2 space sin space straight theta$

$square root of 2 space tan space straight theta$

$square root of 2 space sin space straight theta$

$cos space straight theta space plus space sin space straight theta space equals space square root of 2 space cos space straight theta$
On squaring both sides, we get
$left parenthesis cos space straight theta space plus space sin space straight theta right parenthesis squared space equals space left parenthesis square root of 2 space cos space straight theta right parenthesis squared cos squared space straight theta space plus space sin space squared straight theta space plus space 2 space sin space straight theta space cosθ space equals space 2 space cos squared straight theta 2 space sin space straight theta space cosθ space space equals space cos squared space straight theta space minus space sin space squared straight theta 2 space sin space straight theta space cosθ space space equals space left parenthesis cos space straight theta space minus space sin space straight theta right parenthesis thin space left parenthesis cos space straight theta space plus space sin space straight theta right parenthesis cos space straight theta space minus space sin space space straight theta space equals space fraction numerator 2 space sin space straight theta space cos space straight theta over denominator left parenthesis cos space straight theta space plus space sin space straight theta right parenthesis end fraction space equals fraction numerator 2 space sin space straight theta space cosθ over denominator square root of 2 space cos space straight theta end fraction space equals space square root of 2 space sin space straight theta$

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135.

The value of $fraction numerator 1 over denominator cosec space straight theta space minus space cot space straight theta end fraction space minus space fraction numerator 1 over denominator sin begin display style space end style begin display style straight theta end style end fraction$ is

cot θ
cosec θ
tan θ
1

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136.

If $cos to the power of 4 straight theta space minus space sin to the power of 4 straight theta space equals space 2 over 3 comma space$ then the value of 1 - 2 sin²θ is

0
$2 over 3$
$1 third$
$4 over 3$

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137.

If $tan space straight alpha space equals space straight n space space tan space straight beta space space and space sin space αθ space equals space straight m space sin space straight beta comma space space$ then $cos squared straight alpha$ is

$straight m squared over straight n squared$
$fraction numerator straight m squared minus 1 over denominator straight n squared minus 1 end fraction$
$fraction numerator straight m squared plus 1 over denominator straight n squared plus 1 end fraction$
$fraction numerator straight m squared over denominator straight n squared plus 1 end fraction$

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138.

The value of (tan 1° tan 2° tan 3°.... tan 89°) is

undefined
0
1
89

31 Views

139.

If $straight x space equals space straight a space sec space straight theta space cos space straight ϕ comma space space straight y space equals space straight b space sec space straight theta space sin space straight ϕ$ and $straight z space equals space straight c space tan space straight theta$ . then the value of $straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space straight z squared over straight c squared$

28 Views

140.

If $fraction numerator sec space straight theta space plus space tan space straight theta over denominator sec space straight theta space minus space tan space straight theta end fraction space equals space 5 over 3 comma$ then sin θ is equal to

40 Views

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Multiple Choice Questions

134. If then cos θ - sin θ is