Advertisements
Advertisements
Question
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
Advertisements
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
Prove that:
Show that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
Express each of the following as the product of sines and cosines:
sin 12x + sin 4x
Prove that:
cos 20° + cos 100° + cos 140° = 0
Prove that:
Prove that:
If \[m \sin\theta = n \sin\left( \theta + 2\alpha \right)\], prove that \[\tan\left( \theta + \alpha \right) \cot\alpha = \frac{m + n}{m - n}\]
If A + B = \[\frac{\pi}{3}\] and cos A + cos B = 1, then find the value of cos \[\frac{A - B}{2}\].
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
2 cos `pi/13` cos \[\frac{9\pi}{13} + \text{cos} \frac{3\pi}{13} + \text{cos} \frac{5\pi}{13}\] = 0
