Advertisements
Advertisements
Question
Express the following as the product of sine and cosine.
sin 6θ – sin 2θ
Advertisements
Solution
sin 6θ – sin 2θ
`= 2 cos ((6theta + 2theta)/2) cos ((6theta - 2theta)/2)` ...`[∵ sin "C" - sin "D" = 2 cos (("C + D")/2) cos (("C - D")/2)]`
= 2 cos `((8theta)/2) sin ((4theta)/2)`
= 2 cos 4θ sin 2θ
APPEARS IN
RELATED QUESTIONS
Express each of the following as the product of sines and cosines:
sin 5x − sin x
Express each of the following as the product of sines and cosines:
cos 12x + cos 8x
Prove that:
cos 100° + cos 20° = cos 40°
Prove that:
cos 80° + cos 40° − cos 20° = 0
Prove that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
If sin 2A = λ sin 2B, then write the value of \[\frac{\lambda + 1}{\lambda - 1}\]
Write the value of \[\frac{\sin A + \sin 3A}{\cos A + \cos 3A}\]
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
Prove that:
tan 20° tan 40° tan 80° = `sqrt3`.
