Maths-
General
Easy

Question

I f tan invisible function application x equals b divided by a comma blank t h e n blank square root of open parentheses a plus b close parentheses divided by open parentheses a minus b close parentheses end root plus square root of open parentheses a minus b close parentheses divided by open parentheses a plus b close parentheses end root is equal to

  1. 2 sin invisible function application x divided by square root of sin invisible function application 2 x end root  
  2. 2 cos invisible function application x divided by square root of cos invisible function application 2 x end root  
  3. 2 cos invisible function application x divided by square root of sin invisible function application 2 x end root  
  4. 2 sin invisible function application x divided by square root of cos invisible function application 2 x end root  

The correct answer is: 2 cos invisible function application x divided by square root of cos invisible function application 2 x end root


    sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals sin invisible function application x cos invisible function application x
    rightwards double arrow open parentheses sin to the power of 2 end exponent invisible function application x plus cos to the power of 2 end exponent invisible function application x close parentheses to the power of 2 end exponent minus 2 sin to the power of 2 end exponent invisible function application x cos to the power of 2 end exponent invisible function application x equals sin invisible function application x cos invisible function application x
    rightwards double arrow 1 minus fraction numerator sin to the power of 2 end exponent invisible function application 2 x over denominator 2 end fraction equals fraction numerator sin invisible function application 2 x over denominator 2 end fraction
    rightwards double arrow sin to the power of 2 end exponent invisible function application 2 x plus sin invisible function application 2 x minus 2 equals 0
    rightwards double arrow open parentheses sin invisible function application 2 x plus 2 close parentheses open parentheses sin invisible function application 2 x minus 1 close parentheses equals 0
    rightwards double arrow sin invisible function application 2 x equals 1
    rightwards double arrow 2 x equals open parentheses 4 n plus 1 close parentheses fraction numerator pi over denominator 2 end fraction comma blank n element of Z
    rightwards double arrow x equals open parentheses 4 n plus 1 close parentheses fraction numerator pi over denominator 4 end fraction comma n element of Z
    equals fraction numerator pi over denominator 4 end fraction comma fraction numerator 5 pi over denominator 4 end fraction open parentheses because x element of open square brackets 0 comma blank 2 pi close square brackets close parentheses
    Thus, there are two solutions

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