If $$x3$$−x≥$$2$$ then $$sin$$−$$1x+$$$$sin$$−$$1x2+$$....$$+sin2x10=$$

Question

If $$x3$$−x≥$$2$$ then $$sin$$−$$1x+$$$$sin$$−$$1x2+$$....$$+sin2x10=$$

Infinity Learn · Accepted Answer

Given $$x3$$−x≥$$2$$  ⇒ $$x2$$−$$3x+2$$≤$$0$$  ⇒$$x-1x-2$$≤$$0$$⇒$$1$$≤x≤$$2$$ But $$sin$$$$-1x$$ is defined if $$-1$$≤x≤$$1$$ ⇒$$x=1$$ ∴$$sin$$$$-1x+$$$$sin$$$$-1x2+$$.........$$+$$$$sin$$$$-1x10=$$$$sin$$$$-11+$$$$sin$$$$-11+$$.....$$+$$$$sin$$$$-11$$                                                                            $$=$$π$$2+$$π$$2+$$......$$+$$π$$2$$                                                                             $$=5$$π                                                                             $$=5$$×$$3.14$$                                                                             $$=15.70$$

Introduction to ITF

Remember concepts with our Masterclasses.

If $x (3 - x) \geq 2$ then $\sin^{- 1} (x) + \sin^{- 1} (x^{2}) + .... + \sin^{2} (x^{10}) =$

Ready to Test Your Skills?

free study material

Introduction to ITF

Remember concepts with our Masterclasses.

If x3−x≥2 then sin−1x+sin−1x2+....+sin2x10=

Given x3−x≥2 ⇒ x2−3x+2≤0 ⇒x-1x-2≤0⇒1≤x≤2 But sin-1x is defined if -1≤x≤1 ⇒x=1 ∴sin-1x+sin-1x2+.........+sin-1x10=sin-11+sin-11+.....+sin-11 =π2+π2+......+π2 =5π =5×3.14 =15.70

Ready to Test Your Skills?

free study material

If $x (3 - x) \geq 2$ then $\sin^{- 1} (x) + \sin^{- 1} (x^{2}) + .... + \sin^{2} (x^{10}) =$