Advertisements
Advertisements
Question
Evaluate:
sin 50° – sin 70° + sin 10°
Advertisements
Solution
LHS = (sin 50° – sin 70°) + sin 10°
= 2 cos `((50^circ + 70^circ)/2) sin ((50^circ - 70^circ)/2)` + sin 10°
`[∵ sin "C" - sin "D" = 2 cos (("C + D")/2) sin (("C - D")/2)]`
= 2 cos 60° sin(-10°) + sin 10°
`= 2 xx 1/2` (-sin 10°) + sin 10° ...[∵ sin(-θ) = -sin θ]
= -sin 10° + sin 10°
= 0
= RHS
APPEARS IN
RELATED QUESTIONS
Prove that:
cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A
Prove that:
cos 40° + cos 80° + cos 160° + cos 240° =
If sin α + sin β = a and cos α − cos β = b, then tan \[\frac{\alpha - \beta}{2}\]=
If sin (B + C − A), sin (C + A − B), sin (A + B − C) are in A.P., then cot A, cot B and cot Care in
If \[\tan\alpha = \frac{x}{x + 1}\] and
Prove that:
(cos α – cos β)2 + (sin α – sin β)2 = 4 sin2 `((alpha - beta)/2)`
Evaluate-
cos 20° + cos 100° + cos 140°
