Question

If sin⁻¹x=π/7 for some x ∈(-1,1), then the value of cos⁻¹x=....,Select Proper option from the given options.
(a) 3π/14
(b) 5π/14
(c) π/14
(d) 6π/7

Answer 1

we know, a very popular concepts.
$\bf{sin^{-1}x+cos^{-1}x=\frac{\pi}{2}\qquad|x|\leq1}$

here given, sin^-1x = π/7

so, you can definitely say that,

cos^-1 = π/2 - sin^-1x

= π/2 - π/7

= (7π - 2π)/14

= 5π/14

hence, cos^-1x = 5π/14
therefore, option (b) is correct.

Answer 2

HELLO DEAR,




we know the foumula,
Sin-¹x + cos-¹x = π/2

NOW,
given, sin^-1x = π/7 

sin-¹ + cos-¹x = π/2

π/7 + cos-¹x = π/2

cos-¹ = π/2 - π/7

= (7π - 2π)/14 

= 5π/14 

thus,, cos^-1x = 5π/14 


hence,, option (b) is correct.


I HOPE ITS HELP YOU DEAR,
THANKS