Advertisements
Advertisements
Question
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
Solution
LHS = `(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A")` ...`[∵ cos "C" - cos "D" = - 2 sin (("C + D")/2) sin (("C - D")/2)]`
`= (- 2 sin ((2"A" + 3"A")/2) sin((2"A" - 3"A")/2))/(2 sin ((2"A" + 3"A")/2) cos((2"A" - 3"A")/2))` ...`[∵ sin "C" + sin "D" = 2 sin (("C + D")/2) cos (("C - D")/2)]`
`= (- 2 sin((5"A")/2) sin ((- "A")/2))/(2 sin ((5"A")/2) cos ((- "A")/2))`
`= (2 sin ((5"A")/2) sin ("A"/2))/(2 sin ((5"A")/2) cos (("A")/2))`
= tan `("A"/2)` = RHS
APPEARS IN
RELATED QUESTIONS
Show that :
Prove that:
cos 55° + cos 65° + cos 175° = 0
Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
Prove that:
If cosec A + sec A = cosec B + sec B, prove that tan A tan B = \[\cot\frac{A + B}{2}\].
Prove that:
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0.
If cos A = m cos B, then write the value of \[\cot\frac{A + B}{2} \cot\frac{A - B}{2}\].
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
If sin(y + z – x), sin(z + x – y), sin(x + y – z) are in A.P, then prove that tan x, tan y and tan z are in A.P.
