Question

Prove that

sin50+sin40=$\sqrt{2}$ sin85°​

Answer 1

Answer:

To prove:-

$\sf sin50°+sin40°=\sqrt{2}sin85°$

Proof:-

LHS:-

$\qquad\quad \sf{:}\rightarrowtail sin50°+sin40°$

$\qquad\quad \sf{:}\rightarrowtail sin (45+5)°+sin (45-5)°$

$\qquad\quad \sf{:}\rightarrowtail sin45.cos5+cos45.sin5+sin45.cos5-cos45.sin5$

$\qquad\quad \sf{:}\rightarrowtail \sqrt{2}sin85$

proved

Answer 2

$</p><p>[tex] \\ \\ \\ \\ </p><p>To prove:-</p><p></p><p>\sf sin50°+sin40°=\sqrt{2}sin85°sin50°+sin40°=2sin85° \</p><p></p><p>Proof:- \ </p><p></p><p>LHS:-</p><p></p><p>\qquad\quad \sf{:}\rightarrowtail sin50°+sin40°:↣sin50°+sin40°</p><p></p><p>\qquad\quad \sf{:}\rightarrowtail sin (45+5)°+sin (45-5)°:↣sin(45+5)°+sin(45−5)°</p><p></p><p>\qquad\quad \sf{:}\rightarrowtail sin45.cos5+cos45.sin5+sin45.cos5-cos45.sin5:↣sin45.cos5+cos45.sin5+sin45.cos5−cos45.sin5</p><p></p><p>\qquad\quad \sf{:}\rightarrowtail \sqrt{2}sin85:↣2sin85</p><p></p><p>proved$[/tex]