Enhanced Curriculum Support

Sec A

(1) Draw a rough diagram to the given situation. "A person observed a top of a tree 10 m. away from its foot at the angle of elevation is 45°."

(2) A pole and its shadow have same length, find the angle of the sun ray made with the earth at that time.

(3) Match the following:

(A) Tan q (i) CosqSinq

(B) Cot q (ii) 1+Cot2q

(C) Cosec q (iii) Sec2q−1

(a) A→(i), B→(ii), C→(iii) (b) A→(ii), B→(iii), C→(i)

(c) A→(iii), B→(i), C→(ii) (d) A→(ii), B→(i), C→(iii)

(4) If Δ ABC is right-angled at C, then the value of cos (A + B) is ..... (A) 0 (B) 12 (C) 32 (D) 1

(5) The value of (sin 30° + cos 60°) - (sin 60° + cos 30°) is .....

(A) 0 (B) 1+23 (C) 1−3 (D) 1+3

(6) In △ ABC, ∠B = 90°, then cos(A + C) = ?
(A) 1 (B) 0 (C) 12 (D) 32

(7) Find the value of tan2A, if cos3A=sin45°.

(8) Evaluate cosec 39° · sec 51° - tan 51° · cot 39°.

(9) In a right triangle ABC, right angled at 'C' in which AB = 13 cm, BC = 5 cm, determine the value of cos2B + sin2A.

Sec B

(1) Find sin28212°−sin22212°

(2) From the top of a tower of h m height, Anusha observes the angles of depression of two points X and Y on the same side of tower on the ground to be α and β. Draw the suitable figure for the given information.

(3) From the top of the building the angle of elevation of the top of the cell tower is 60° and the angle of depression to its foot is 45°, if the distance of the building from the tower is 30 meters, draw the suitable diagram to the given data.

(4) "The top of a tower is observed at an angle of elevation 45° and the foot of the tower is at a distance of 30 metres from the observer". Draw a suitable diagram for this data.

(5) "An observer standing at a distance of 10m from the foot of a tower, observes its top with an angle of elevation of 60°". Draw a suitable diagram for this situation.

(6) "An observer standing at a distance of 50 metre from the foot of a tower observes its top at an angle of elevation of 45°." Draw a suitable diagram for this situation.

(7) If Tan Q = 724, then find the value of Sec Q.

(8) Prove that sin 78° + cos 132° = 5−14

(9) Express tan θ in terms of sin θ.

(10) Express 'sin θ' in terms of 'tan θ'.

(11) Express 'tan θ' in terms of 'sin θ'.

(12) Find measure of the angles A and B, if cosA−B=32 and sinA+B=32.

(13) Find the value of tan260°+cot230°sin230°+cos260°

Sec C

(1) In △ABC, if a : b : c = 7 : 8 : 9, then find cosA : cosB : cosC

(2) Solve that equation sinx+3cosx = 2

(3) Prove that tan−112 + tan−115 + tan−118 = π4

(4) Prove that tan70° - tan20° = 2tan50°

Sec D

(1) Prove that sinθ1+cosθ + 1+cosθsinθ = 2 cosec θ

(2) Express the following in terms of trigonometric ratios of angles between 0° and 45°:

(i) Sin 81° + Tan 75° (ii) Cos 65° + Cot 75°

(3) Show that: 1+tan2A1+cot2A – 1−tanA1−cotA = tan2A

(4) Prove that: cosA1−tanA+sinA1−cotA=sinA+cosA

OR

Show that: secθ−tanθ2=1−sinθ1+sinθ

(5) Show that : cosθ1−sinθ+1−sinθcosθ=2secθ

OR

In a right angle triangle, the hypotenuse is 10 cm more than the shortest side. If third side is 6 cm less than the hypotenuse, find the sides of the right angle triangle.

Sec E

(1) In an acute angled triangle ABC, if sin(A + B - C) = 12 and cos(B + C - A) = 12, then find ∠A, ∠B and ∠C.

(2) If sec θ + tan θ = P, then prove that sin θ = P2−1P2+1.