(1) Express each of the following as a sum or difference
(i) sin 35°cos 28°
(ii) sin 4x cos 2x
(iii) 2 sin 10θ cos 2θ
(iv) cos 5θ cos 2θ
(v) sin 5θ sin 4θ Solution
(2) Express each of the following as a product
(i) sin 75° − sin 35°
(ii) cos 65° + cos 15°
(iii) sin 50° + sin 40°
(iv) cos 35° − cos 75° Solution
(3) Show that sin 12° sin 48° sin 54° = 1/8 Solution
(4) Show that
cos π/15 cos 2π/15 cos 3π/15 cos 4π/15 cos 5π/15 cos 6π/15 cos 7π/15 = 1/128 Solution
(5) Show that
(sin8x cosx-sin6x cos3x)/(cos2x cosx-sin3x sin4x) = tan2x
(6) Show that
(cosθ−cos3θ) (sin8θ+sin2θ)/(sin5θ−sinθ) (cos4θ−cos6θ)=1
(7) Prove that sin x + sin2x + sin3x = sin2x (1 + 2cos x).
(8) Prove that
(sin 4x + sin2x) /(cos 4x + cos2x) = tan3x. Solution
(9) Prove that
1 + cos2x + cos4x + cos6x = 4cos x cos 2x cos 3x.
(10) prove that
sin θ/2 sin 7θ/2 + sin 3θ/2 sin 11θ/2 = sin2θ sin 5θ.
(11) Prove that
cos (30°−A) cos (30°+A) + cos (45°−A) cos (45°+A) = cos2A + (1/4) Solution
(12) Prove that
(sin x + sin3x + sin5x + sin7x) / (cos x + cos3x + cos5x + cos7x) = tan4x. Solution
(13) Prove that
sin (4A − 2B) + sin(4B − 2A) /cos (4A − 2B) + cos (4B − 2A)
= tan(A + B). Solution
(14) Show that cot (A + 15) − tan (A − 15) = 4 cos 2A/1+2sin2A Solution
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