Prove that —Sin A + Sin B/Cos A + Cos B equals to Tan (A+B/2)
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Answer:
Step-by-step explanation:
L.H.S. =
cosA+cosB
sinA−sinB
+
sinA+sinB
cosA−cosB
⇒ L.H.S. =
(cosA+cosB)(sinA+sinB)
(sinA−sinB)(sinA+sinB)+(cosA+cosB)(cosA−cosB)
⇒ L.H.S. =
(cosA+cosB)(sinA+sinB)
sin
2
A−sin
2
B+cos
2
A−cos
2
B
⇒ L.H.S. =
(cosA+cosB)(sinA+sinB)
(sin
2
A+cos
2
A)−(sin
2
B+cos
2
B)
⇒ L.H.S. =
(cosA+cosB)(sinA+sinB)
1−1
=0=R.H.S.
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