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
Prove that:
Prove that:
Prove that:
tan 20° tan 40° tan 60° tan 80° = 3
Prove that:
Prove that:
sin (B − C) cos (A − D) + sin (C − A) cos (B − D) + sin (A − B) cos (C − D) = 0
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 \[\tan\alpha = \frac{x}{x + 1}\] and
Express the following as the sum or difference of sine or cosine:
cos 7θ sin 3θ
Express the following as the product of sine and cosine.
cos 2θ – cos θ
Prove that:
`(cos 2"A" - cos 3"A")/(sin "2A" + sin "3A") = tan "A"/2`
