Advertisements
Advertisements
प्रश्न
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
Advertisements
उत्तर
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
संबंधित प्रश्न
Prove that:
Prove that
\[\tan x \tan \left( \frac{\pi}{3} - x \right) \tan \left( \frac{\pi}{3} + x \right) = \tan 3x\]
Express each of the following as the product of sines and cosines:
sin 2x + cos 4x
Prove that:
If sin A + sin B = α and cos A + cos B = β, then write the value of tan \[\left( \frac{A + B}{2} \right)\].
If \[\tan\alpha = \frac{x}{x + 1}\] and
Prove that:
cos 20° cos 40° cos 80° = `1/8`
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
If cosec A + sec A = cosec B + sec B prove that cot`(("A + B"))/2` = tan A tan B.
