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:
cos 40° cos 80° cos 160° = \[- \frac{1}{8}\]
Prove that:
cos 20° cos 40° cos 80° = \[\frac{1}{8}\]
Prove that:
sin 10° sin 50° sin 60° sin 70° = \[\frac{\sqrt{3}}{16}\]
Prove that:
Prove that:
cos 3A + cos 5A + cos 7A + cos 15A = 4 cos 4A cos 5A cos 6A
Prove that:
Prove that:
Write the value of the expression \[\frac{1 - 4 \sin 10^\circ \sin 70^\circ}{2 \sin 10^\circ}\]
Find the value of tan22°30′. `["Hint:" "Let" θ = 45°, "use" tan theta/2 = (sin theta/2)/(cos theta/2) = (2sin theta/2 cos theta/2)/(2cos^2 theta/2) = sintheta/(1 + costheta)]`
