Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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
10 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
one year 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
one year ago
Feel free to ask querry 
We will happy to help you.
Good Luck 
Cheers ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
 
Kushagra Madhukar
askIITians Faculty 629 Points
one year 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
 
 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free