If $$2sin$$⁡$$A2=1+$$$$sin$$⁡$$A+1$$−$$sin$$⁡A, then $$A2lies$$ between

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If $$2sin$$⁡$$A2=1+$$$$sin$$⁡$$A+1$$−$$sin$$⁡A, then $$A2lies$$ between

Infinity Learn · Accepted Answer

We have,$$2sin$$⁡$$A2=1+$$$$sin$$⁡$$A+1$$−$$sin$$⁡A⇒$$2sin$$⁡$$A2=($$$$cos$$⁡$$A/2+$$$$sin$$⁡$$A/2)2$$                                          $$+($$$$cos$$⁡$$A/2$$−$$sin$$⁡$$A/2)2$$⇒$$2sin$$⁡$$A/2=$$|$$cos$$⁡$$A/2+$$$$sin$$⁡$$A/2$$|                                                               $$+$$|$$cos$$⁡$$A/2$$−$$sin$$⁡$$A/2$$|⇒$$cos$$⁡$$A/2+$$$$sin$$⁡$$A/2$$≥$$0$$ and $$cos$$⁡$$A/2$$−$$sin$$⁡$$A/2$$≤$$0$$⇒π$$/4$$≤$$A/2$$≤$$3$$π$$/4$$ and π$$/4$$≤A≤$$5$$π$$/4$$⇒π$$/4$$≤$$A/2$$≤$$3$$π$$/4$$⇒$$2n$$π$$+$$π$$/4$$≤$$A/2$$≤$$2n$$π$$+3$$π$$/4$$,n∈Z.

If $2 \sin \frac{A}{2} = \sqrt{1 + \sin A} + \sqrt{1 - \sin A},$ then $\frac{A}{2}$ lies between

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If 2sin⁡A2=1+sin⁡A+1−sin⁡A, then A2lies between

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If $2 \sin \frac{A}{2} = \sqrt{1 + \sin A} + \sqrt{1 - \sin A},$ then $\frac{A}{2}$ lies between