### (Sample Printed worksheet)

1)Simplify 3(sin4θ + cos4θ) - 2(sin6θ + cos6θ)
 2) Simplify cos3θ sin3(90°-θ) + sin3θ cos3(90°-θ) + 3 cos2θ sin2θ
 3) If α + β = 90°, simplify .
 4) Simplify
 5) Simplify

### Choose correct answer(s) from given choice

6)(cosθ - secθ)(cosecθ - sinθ) = ?
a. sinθ cosθ b.
 -1 sinθ cosθ

c.
 1 sinθ cosθ

d. - sinθ cosθ
7)A 2√3 m high pole casts 2 m long shadow on the ground. Find the angle of Sun's elevation.
 a. 60° b. 30° c. 45° d. 37.5°
8)A spherical balloon of radius 15 feet subtends an angle 60° at the eye of an observer. If the angle of elevation of its centre is 30°, find the height of the centre of the balloon.
 a. feet b. feet c. feet d. feet
9)If cosec θ = a/b and 0° > θ > 90°, find value of cot θ.
 a. b. c. d.
10)Simplify
 a. cos2θ - sin2θ b. sinθ + cosθ c. sin2θ - cos2θ d. sinθ - cosθ

1) 1
 Step 1 = 3 (sin4θ + cos4θ) - 2 [ (sin2θ)3 + (cos2θ)3 } ] Step 2 = 3 (sin4θ + cos4θ) - 2 [ (sin2θ + cos2θ) {(sin2θ)2 + (cos2θ)2 - sin2θ cos2θ } ] Step 3 Since sin2θ + cos2θ = 1 =3 (sin4θ + cos4θ) - 2 {sin4θ + cos4θ - sin2θ cos2θ } Step 4 = sin4θ + cos4θ + 2 sin2θ cos2θ Step 5 = (sin2θ + cos2θ)2 = 12 = 1

2) 1
 Step 1 Since sin(90°-θ) = cos θ and cos(90°-θ) = sin θ, expression can be rewritten as following= (cos2θ)3 + (sin2θ)3 + 3 cos2θ sin2θ Step 2 Since x3 + y3 = ( x + y ) ( x2 + y2 - xy) = (cos2θ + sin2θ ) [ (cos2θ)2 + (sin2θ)2 - cos2θ sin2θ ] + 3 cos2θ sin2θ Step 3 Since cos2θ + sin2θ =1 and x2 + y2 = (x+y)2 - 2 xy) = (cos2θ + sin2θ ) [ (cos2θ + sin2θ)2 - 2 cos2θ sin2θ - cos2θ sin2θ] + 3 cos2θ sin2θ = [ 1 - 3 cos2θ sin2θ ] + 3 cos2θ sin2θ = 1

3) ± cos α
 Step 1 It is given that α + β = 90°, therefore β = 90° - α Step 2 Replace β with 90° - α in given expression S = ⇒ S = Step 3 Using trigonometrical identities ⇒ S = ⇒ S = ⇒ S = ± cos α

4) 0
 Step 1 On adding two fractions= Step 2 = Step 3 = Step 4 =

5) 2 tanθ
 Step 1 = Step 2 = Step 3 =

6) d. - sinθ cosθ
7) a. 60°
 Step 1 In following figure, AC shows the pole and AB is its shadow, and angle ∠B is the angle of Sun's elevation. Step 2 tan(∠B) = AC/AB ⇒ tan(∠B) = (2√3)/(2) ⇒ tan(∠B) = √3 Step 3 We know that tan(60°) = √3, therefore, ⇒ ∠B = 60°

8) d. feet
9) d.
 Step 1 We know that,cot θ = √(cosec2θ - 1) Step 2 Now replace value of cosec(θ) in above equation ⇒ cot(θ) = Step 3 Simplify RHS of above equation ⇒ cot(θ) =

10) b. sinθ + cosθ