Grade 12Trigonometry

solve for x
cos^-1(x) + sin^-1(x/2) = pi/6

taniska

12 Years agoGrade 12

3 Answers

Sher Mohammad

12 Years ago

take sin for both sides,

sin(cos^-1(x) + sin^-1(x/2) )= sin(pi/6)

sin(cos^-1(x))cos(sin^-1(x/2))+sin(sin^-1(x/2) ))cos(cos^-1(x))=.5

sqrt(1-cos(cos^-1(x)))^2)sqrt(1-sin(sin^-1(x/2)))^2)+x^2/2=.5

sqrt(1-x^2)sqrt(1-(x/2)^2)+x^2/2=.5

now , solve for x

sher mohammad

b.tech, iit delhi

moon

7 Years ago

We have cos–1x + sin–1 




2
x
=
6

cos–1x =
6

– sin–1x
 x = cos 



 
2
x
– sin
6
–1
= cos
6

cos 




2
x
sin–1
+ sin
6

sin 




2
x
sin–1
 x =
2
3
cos 2
x
·
2
1
4
x
cos 1–
2
–1  



 


 x =
4
x
4
x
1–
2
3 2

 x –
4
x
=
4
x
1–
2
3 2

4
x
1–
2
3
4
3x 2
  



 



4
x
1–
4
3
16
9x2 2

4
3x2
= 1 –
4
x2

4
x
4
3x2 2
 = 1

4
4x2
= 1
 x2 = 1  x = ±1 But x = 1