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find value of sin{1/4(sin inverse(63^1/2)/8))} is ___________ ans: 1/2.2^1/2

find value of sin{1/4(sin inverse(63^1/2)/8))} is ___________


 


ans: 1/2.2^1/2

Grade:12

2 Answers

Vinay Arya
37 Points
13 years ago

Hi Shefall Sharma

631/2 is nearly equal to 8.

sin{[sin-1(631/2/8)]/4}=sin(90o/4)=sin(45o/2)               

We know that cos2A = 1-2sin2A

    Putting A=45o/2

   cos45o=1-2sin2(45o/2)=>sin(45o/2)= [(21/2-1)/21/2]1/2

 Therefore, sin{[sin-1(631/2/8)]/4}=[(21/2-1)/21/2]1/2

Rajput adarsh
11 Points
6 years ago
sin(1/4 sin^-1(√63/8)        =   let sin^-1(√63/8) be equal to a   I.e.  sin^-1(√63/8) =a                                                          therefore      sina=√63/8       now put this value in question                                                       sin(a/4)    we can find the value of cos( a) = 2cos^2(a/2) -1        by forming triangle                                1/8 +1 =     2 cos^2(a/2)                                                                      cos(a)=1/8     (answer)                         cos(a/2)= ¾   hence similarly finding cos(a/4)=√7/2√2        hence  s
in(a/4) = 1/2√2

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