# TRIGONOMETRY WORKSHEET FOR GRADE 11

(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

Solution

(6)  Show that

(cosθ−cos3θ) (sin8θ+sin2θ)/(sin5θ−sinθ) (cos4θ−cos6θ)=1

Solution

(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.

Solution

(10)  prove that

sin θ/sin 7θ/+ sin 3θ/sin 11θ/2 = sin2θ sin 5θ.

Solution

(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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