Question

what is the value of question given in photo Q. 20​

Answer 1

Answer:

Lets us assume cos^-1 (7/25) = x                   ------->   (1)

Therefore,

7/25=cos x

or cos x =7/25                                                  ------->   (2)

Squaring both sides:

=> cos^2 x = (7/25)^2

=> 1 - sin^2 x =(7/25)^2                              as sin^2 x+cos^2 x = 1

=> sin^2 x = 1 - (7/25)^2

Taking square root both sides:

=>sin x = sqrt[1 - (7/25)^2]                                 ------> (3)

Getting back to original equation and putting the assumed equation (1):

cot[cos^-1 (7/25) = cot x

cot x = cos x / sin x

Putting equation (2) and (3):

cot[cos^-1 (7/25)  

=  {(7/25)/ sqrt[1 - (7/25)^2] }

=  {(7/25)/ sqrt[1 - 49/625] }

=  {(7/25)/ sqrt[(625- 49)/625] }

=  {(7/25)/ sqrt[576/625] }

=  {(7/25)/ (24/25) }

= 7/24   --------------> required value