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What is the value of Cos(2Cos -1 x+Sin -1 x) at x=1/5?

What is the value of Cos(2Cos-1x+Sin-1x) at x=1/5?

Grade:12

4 Answers

vikas askiitian expert
509 Points
12 years ago

cos-1x + sin-1x = pi/2   ............1                   (identity)

 

cos(2cos-1x+sin-1x) = cos[(cos-1x+sin-1x) + cos-1x]

=cos[pi/2 + cos-1x]                             (by using eq 1)

 

(    we know , cos[pi/2+A] = -sinA   )

 

=-sin[cos-1x]

=-sin[sin-1(1-x2)1/2]                              (cos-1x = sin-1(1-x2)1/2  )

=-(1-x2)1/2 

at x = 1/5

=-(2root6)/5

 

Krish Gupta
askIITians Faculty 82 Points
2 years ago
It’s just a play of some equations :  

cos-1x + sin-1x = pi/2   ............1                   (identity)

 

cos(2cos-1x+sin-1x) = cos[(cos-1x+sin-1x) + cos-1x]

=cos[pi/2 + cos-1x]                             (by using eq 1)

 

(    we know , cos[pi/2+A] = -sinA   )

 

=-sin[cos-1x]

=-sin[sin-1(1-x2)1/2]                              (cos-1x = sin-1(1-x2)1/2  )

=-(1-x2)1/2 

at x = 1/5

=-(2root6)/5

Vikas TU
14149 Points
2 years ago
Feel free to ask querry 
We will happy to help you.
Good Luck 
Cheers ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
 
Kushagra Madhukar
askIITians Faculty 628 Points
2 years ago
Dear student,
Please find the attached answer to your problem.
 
 cos[2cos-1x + sin-1x] = cos[(cos-1x + sin-1x) + cos-1x] = cos[π/2 + cos-1x]
= – sin[cos-1x] = – (1 – x2)½           (Identity)
 = – (1 – [1/5]2)½   = 2√6/5
 
Hope it helps.
Thanks and regards,
Kushagra
 
 

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