Question

find the value of x is if sin sin^(-1)((x)/(5))+cos^(-1)((3)/(5)) =1​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \sin \bigg( { \sin}^{ - 1} \frac{x}{5} + { \cos}^{ - 1} \frac{3}{5} \bigg) = 1 }$

TO DETERMINE

The value of x

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{ \bigg( { \sin}^{ - 1} x+ { \cos}^{ - 1}x\bigg) = \frac{\pi}{2} }$

EVALUATION

$\displaystyle \sf{ \sin \bigg( { \sin}^{ - 1} \frac{x}{5} + { \cos}^{ - 1} \frac{3}{5} \bigg) = 1 }$

$\displaystyle \sf{ \implies \: \bigg( { \sin}^{ - 1} \frac{x}{5} + { \cos}^{ - 1} \frac{3}{5} \bigg) = { \sin}^{ - 1} 1 }$

$\displaystyle \sf{ \implies \: \bigg( { \sin}^{ - 1} \frac{x}{5} + { \cos}^{ - 1} \frac{3}{5} \bigg) = \frac{\pi}{2} }$

$\displaystyle \sf{ \implies \: { \sin}^{ - 1} \frac{x}{5} = \frac{\pi}{2} - { \cos}^{ - 1} \frac{3}{5} }$

$\displaystyle \sf{ \implies \: { \sin}^{ - 1} \frac{x}{5} = { \sin}^{ - 1} \frac{3}{5} }$

$\implies \sf{x = 3}$

FINAL ANSWER

Hence the required value of x = 3

tan⁻¹(x/y)-tan⁻¹(x-y/x+y)=...(x/y≥0),Select Proper option from the given options.

(a) π/4

(b) π/3

(c) π/2

(d) π

https://brainly.in/question/5596504

2. tan⁻¹2 +tan⁻¹3 is..,Select Proper option from the given options.

(a) - π/4

(b) π/2

(c) 3π/4

(d) 3π/2

https://brainly.in/question/5596487

Answer 2

Step-by-step explanation:

Hence the required value of x = 3