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If $2 space sin space open parentheses πx over 2 close parentheses space equals space straight x squared space plus space 1 over straight x squared comma$ then the value of $open parentheses straight x minus 1 over straight x close parentheses$ is

-1
2
1
1

134 Views

62.

If $0 degree space less than space straight theta space less than space 90 degree$ , the value of sin θ + cos θ is

equal to 1
greater than 1
less than 1
less than 1

164 Views

63.

If θ is a positive acute angle and tan 2θ tan 3θ = 1, then the value of
$left parenthesis 2 space cos squared straight theta fraction numerator 5 straight theta over denominator 2 end fraction minus 1 right parenthesis$ is

$negative 1 half$
1
0
0

188 Views

64.

If $sin space 17 degree space equals space straight x over straight y comma$ then the value of $left parenthesis sec space 17 degree space minus space sin space 73 degree right parenthesis$ is

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

124 Views

65.

In a right-angled triangle, XYZ, right-angled at Y, If $XY space equals space 2 square root of 6$ and XZ - YZ = 2, then sec X + tan X is

$fraction numerator 1 over denominator square root of 6 end fraction$
$square root of 6$
$2 square root of 6$
$2 square root of 6$

311 Views

66.
If tan θ - cot θ = 0 and θ is positive acute angle, then the value of $fraction numerator tan space left parenthesis straight theta space plus space 15 degree right parenthesis over denominator tan space left parenthesis straight theta space minus 15 degree right parenthesis end fraction$ is

3

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

tan space straight theta space minus space cot space straight theta space equals space 0 rightwards double arrow space space tan space straight theta space equals space cot space straight theta rightwards double arrow space space tan space straight theta space equals space tan space left parenthesis 90 degree minus straight theta right parenthesis rightwards double arrow space space straight theta space equals space 90 degree space minus straight theta rightwards double arrow space 2 straight theta space equals space 90 degree rightwards double arrow space space straight theta space equals space 45 degree

therefore space space space space fraction numerator tan left parenthesis straight theta space plus space 15 degree right parenthesis over denominator tan left parenthesis straight theta minus 15 degree right parenthesis end fraction

equals space fraction numerator tan left parenthesis 45 degree space plus 15 degree right parenthesis over denominator tan left parenthesis 45 degree minus 15 degree right parenthesis end fraction space equals fraction numerator tan space 60 degree over denominator tan space 30 degree end fraction equals space fraction numerator square root of 3 over denominator begin display style fraction numerator 1 over denominator square root of 3 end fraction end style end fraction space equals space square root of 3 space cross times space square root of 3 space equals space 3

173 Views

67.

If $sec space straight theta space minus space tan space straight theta space equals space fraction numerator 1 over denominator square root of 3 end fraction comma$ the value of $sec space straight theta. space space tan space straight theta$ is

$2 over 3$
$fraction numerator 2 over denominator square root of 3 end fraction$
$fraction numerator 4 over denominator square root of 3 end fraction$
$fraction numerator 4 over denominator square root of 3 end fraction$

359 Views

68.

If $5 space cos space straight theta space plus space 12 space sin space straight theta space equals space 13$ , $0 degree less than straight theta less than 90 degree comma$ then the value of $sin space straight theta$ is