If α,β,γ∈$$0$$,π$$2$$ then the value of $$sin$$⁡$$($$α$$+$$β$$+$$γ$$)$$$$sin$$⁡α$$+$$$$sin$$⁡β$$+$$$$sin$$⁡γ is

Question

If α,β,γ∈$$0$$,π$$2$$ then the value of $$sin$$⁡$$($$α$$+$$β$$+$$γ$$)$$$$sin$$⁡α$$+$$$$sin$$⁡β$$+$$$$sin$$⁡γ is

Infinity Learn · Accepted Answer

$$sin$$⁡$$($$α$$+$$β$$+$$γ$$)=$$$$sin$$⁡α$$cos$$⁡β$$cos$$⁡γ$$+$$$$cos$$⁡α$$sin$$⁡β$$cos$$⁡γ$$+$$$$cos$$⁡α$$cos$$⁡β$$sin$$⁡γ−$$sin$$⁡α$$sin$$⁡β$$sin$$⁡γ ⇒$$sin$$⁡$$($$α$$+$$β$$+$$γ$$)$$−$$sin$$⁡α−$$sin$$⁡β−$$sin$$⁡γ $$=$$$$sin$$⁡α$$($$$$cos$$⁡β$$cos$$⁡γ−$$1)+$$$$sin$$⁡β$$($$$$cos$$⁡α$$cos$$⁡γ−$$1)+$$$$sin$$⁡γ$$($$$$cos$$⁡α$$cos$$⁡β−$$1)$$−$$sin$$⁡α$$sin$$⁡β$$sin$$⁡γ ⇒ $$sin$$⁡$$($$α$$+$$β$$+$$γ$$)$$−$$sin$$⁡α−$$sin$$⁡β−$$sin$$⁡γ<$$0$$⇒ $$sin$$⁡$$($$α$$+$$β$$+$$γ$$)$$

If $α, β, γ \in (0, \frac{π}{2})$ then the value of $\frac{\sin (α + β + γ)}{\sin α + \sin β + \sin γ}$ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If α,β,γ∈0,π2 then the value of sin⁡(α+β+γ)sin⁡α+sin⁡β+sin⁡γ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $α, β, γ \in (0, \frac{π}{2})$ then the value of $\frac{\sin (α + β + γ)}{\sin α + \sin β + \sin γ}$ is