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

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

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

2 over 3

If $sec space straight theta space minus space tan space straight theta space equals space fraction numerator 1 over denominator square root of 3 end fraction$ ...(i)
Then, $sec space straight theta space plus space tan space straight theta space equals space fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator square root of 3 end fraction end style end fraction space space space equals space square root of 3 space$ ...(ii)
$open square brackets because space space sec space straight theta space minus space tan space straight theta space equals space fraction numerator 1 over denominator sec space straight theta space plus space tan space straight theta end fraction close square brackets$
Adding (i) and (ii),
$2 space sec space straight theta space space equals space square root of 3 space space plus space fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator 3 plus 1 over denominator square root of 3 end fraction space equals space fraction numerator 4 over denominator square root of 3 end fraction space space rightwards double arrow space space secθ space equals space fraction numerator 2 over denominator square root of 3 end fraction$
Again, by equation (ii) - (i)
$2 space tan space straight theta space equals space square root of 3 space minus space fraction numerator 1 over denominator square root of 3 end fraction space equals space fraction numerator 3 minus 1 over denominator square root of 3 end fraction space equals space fraction numerator 2 over denominator square root of 3 end fraction$
$rightwards double arrow space space space tan space straight theta space equals space fraction numerator 1 over denominator square root of 3 end fraction$
$therefore space space space sec space straight theta space. space tan space straight theta equals space fraction numerator 2 over denominator square root of 3 end fraction space cross times space fraction numerator 1 over denominator square root of 3 end fraction space equals space 2 over 3$

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