If  and  then the value of  is from Quantitative Aptitude

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 Multiple Choice QuestionsMultiple Choice Questions

71.

The value of left parenthesis cosec space straight alpha space minus space sin space straight alpha right parenthesis space space left parenthesis sec space straight alpha minus cos space straight alpha right parenthesis space left parenthesis tan space straight alpha space plus space cot space straight alpha right parenthesis

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  • 6

  • 2

  • 2

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72.

If x =  a sin θ - b cos θ,  y = a cos θ + b sin θ, then which of the following is true?

  • straight x squared over straight y squared space plus space straight a squared over straight b squared space equals space 1
  • straight x squared space plus space straight y squared space equals space straight a squared space minus space straight b squared
  • straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space 1
  • straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space 1
351 Views

73.

The value of 
cot 41°. cot 42°. cot 43°. cot 44°. cot 45°. cot 46°. cot 47°. cot 48°. cot 49°.

  • 1

  • 0

439 Views

74.

If tan A = n tan B and sin A = m sin B, then the value of cos2A is

  • fraction numerator straight m squared minus 1 over denominator straight n squared plus 1 end fraction
  • fraction numerator straight m squared plus 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 plus 1 over denominator straight n squared plus 1 end fraction
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75.

The value of the expression
(1 + sec 22° + cot 68°) (1 - cosec 22° + tan 68°) is

  • 0

  • 1

  • -1

  • -1

1505 Views

76.

If straight x space sin cubed straight theta space plus space straight y space cos cubed straight theta space equals space space sin space straight theta space cos space straight theta and straight x space sin space straight theta space minus space straight y space cos space straight theta equals space space 0 comma then the value of left parenthesis straight x squared plus straight y squared right parenthesis equals

  • 1

  • 1 half
  • 3 over 2
  • 3 over 2
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77.

If sec space straight theta space space plus space tan space straight theta space equals space straight m space left parenthesis greater than 1 right parenthesis comma then the value of sin space straight theta left parenthesis 0 degree space less than thin space straight theta space less than space 90 degree right parenthesis is:

  • fraction numerator 1 minus straight m squared over denominator 1 plus straight m squared end fraction
  • fraction numerator straight m squared minus 1 over denominator straight m squared plus 1 end fraction
  • fraction numerator straight m squared plus 1 over denominator straight m squared minus 1 end fraction
  • fraction numerator straight m squared plus 1 over denominator straight m squared minus 1 end fraction
509 Views

78.

If left parenthesis straight a squared minus straight b squared right parenthesis space sin space straight theta space plus space 2 ab space cosθ space equals space straight a squared space plus space straight b squared comma space then space tanθ space equals space thin space ?

  • fraction numerator 2 ab over denominator straight a squared minus straight b squared end fraction
  • fraction numerator straight a squared minus straight b squared over denominator 2 ab end fraction
  • fraction numerator ab over denominator straight a squared minus straight b squared end fraction
  • fraction numerator ab over denominator straight a squared minus straight b squared end fraction
419 Views

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79.

If 2 straight y space cosθ space equals space straight x space sinθ and 2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 comma then the value of open parentheses straight x squared space plus space 4 straight y squared close parentheses is

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  • 2

  • 3

  • 3


D.

3

2 straight y space cosθ space equals space straight x space sin space straight theta space space space space space space  ...(i)
rightwards double arrow space space space space straight x space equals space fraction numerator 2 straight y space cosθ over denominator sin space straight theta end fraction space space space space space... left parenthesis ii right parenthesis
2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 
rightwards double arrow space space space 2. space fraction numerator 2 straight y space cosθ over denominator sin space straight theta end fraction. space sec space straight theta space minus space straight y space cosec space straight theta space space equals space 3 space space space space space left square bracket Using space left parenthesis ii right parenthesis right square bracket
rightwards double arrow space space space 4 straight y space cosec space straight theta space minus space straight y space coecθ space equals space 3
rightwards double arrow space space space 3 straight y space cosec space straight theta space equals space 3
rightwards double arrow space space space space space straight y space equals space fraction numerator 3 over denominator 3 cosec space straight theta end fraction equals space space sin space straight theta
From equation (i),
2 space sin space straight theta space. space cos space straight theta space equals space straight x space sin space straight theta
rightwards double arrow space space space space straight x space equals space 2 space cosθ
therefore space space space space space space straight x squared space plus space 4 straight y squared space equals space 4 space cos squared straight theta space plus space 4 space sin squared straight theta
space space space space equals space 4 left parenthesis cos squared straight theta space plus space sin squared straight theta right parenthesis
space space space space equals space 4
 
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80.

The expression of
fraction numerator cot space straight theta space plus space cosec space straight theta space minus space 1 over denominator cot space straight theta space minus space cosec space straight theta space plus space 1 end fraction is equal to

  • fraction numerator 1 plus cos space straight theta over denominator sin space straight theta end fraction
  • fraction numerator 1 minus cos space straight theta over denominator sin space straight theta end fraction
  • fraction numerator cot space straight theta space plus space 1 over denominator cosec space straight theta end fraction
  • fraction numerator cot space straight theta space plus space 1 over denominator cosec space straight theta end fraction
547 Views

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