Grade 12Trigonometry

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

ans: 1/2.2^1/2

shefali sharma

16 Years agoGrade 12

2 Answers

Vinay Arya

16 Years ago

Hi Shefall Sharma

63^1/2is nearly equal to 8.

sin{[sin^-1(63^1/2/8)]/4}=sin(90^o/4)=sin(45^o/2)

We know that cos2A = 1-2sin²A

Putting A=45^o/2

cos45^o=1-2sin²(45^o/2)=>sin(45^o/2)= [(2^1/2-1)/2^1/2]^1/2

Therefore, sin{[sin^-1(63^1/2/8)]/4}=[(2^1/2-1)/2^1/2]^1/2

Rajput adarsh

8 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