Practice these Questions for the upcoming board exam.

Q.1 If cotθ=\frac{7}{8}

Evaaluate

(i) \frac{(1+sinθ)(1-sinθ)}{(1+cosθ)(1-cosθ)}

(ii) cot²θ

Answer:

(i) \frac{49}{64}

(ii) \frac{49}{64}

Q.2 In ΔPQR, right-angled at Q, PR+QR=25cm and PQ=5cm. Determine the values of sinP,cosP, and tanP.

Answer : sinP=\frac{12}{13},cosP=\frac{5}{13} and tanP=\frac{12}{5}

Q.3 If ∠A and ∠B are acute angles such that cosA=cosB, then show that ∠A =∠B

Q.4 State whether the following are true or false.Justify your answer

(i) The value of tanA is always less than 1

(ii) SecA=\frac{12}{5} for some value of angle A

(iii) cos A is the abbreviation used for the cosecant of angle A

(iv) CotA is the product of CotA and A

(v) sinθ=\frac{4}{3} for some angle θ

Answer:

(i) false

(ii) true

(iii) false

(iv) false

(v) false

Q.5 If tan(A+B)=√3 and tan(A-B)=\frac{1}{√3} ; 0º<A+B≤90º;A>B. Find A and B

Answer: ∠A=45º , ∠B=15º

Q.6 Evaluate \frac{tan65º}{cot25º}

Answer: 1

Q.7 If sin3A=cos(A-26º), where 3A is an acute angle, find the value of A.

Answer: A=29º

Q.8 Show that

tan48º tan 23º tan42º tan67º=1

Q.9 If tanA=CotB ,prove that A+B=90º

Q.10 If A,B and C are interior angles of a triangle ABC,then show that

sin(\frac{B+C}{2})=cos\frac{A}{2}

Q.11 Express the trigonometric ratios sinA,secA, and tanA in terms of cotA.

Q.12 Here are some identities which you can practice

(i) Prove that \frac{sinθ-cosθ+1}{sinθ+cosθ-1}=\frac{1}{secθ-tanθ} ,using the identity sec²θ=1+tan²θ.

(ii) \frac{tanθ}{1-cotθ}+\frac{cotθ}{1-tanθ}=1+secθ cosecθ

(iii) \frac{cosA-sinA+1}{cosA+sinA-1}=cosecA+cotA ,using the identity cosec²A=1+cot²A

(iv) \frac{sinθ-2sin²θ}{2cos³θ-cosθ}=tanθ

(v) (sinA+cosecA)²+(cosA+secA)²=7+tan²A+cot²A

If you want to practice more questions on trigonometric identities check this

## Application of trigonometry Questions

Q.1 A tower stands vertically on the ground. From a point on the ground which is 15m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60º. Find the height of the tower

**Ans.15√3 m**

Q.2 From a point P on the ground the angle of the elevation of the top of a 10m tall building is 30º. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45º. Find the length of the flagstaff and the distance of the building from point P.(you may take √3=1.732).

**Ans.** The length** of the flagstaff and distance of the building are 7.32m and 17.32m **

Q.3 The shadow of a tower standing on the level ground is found to be 40 m longer when the sun’s altitude is 30º than when it is 60º. Find the height of the tower?

**Ans. Height of the tower=20√3m**

Q.4 Two poles of equal heights are standing opposite each other on either side of the road, which is 80m wide . From a point between them on the road, the angle of elevation of the top of the poles is 60º and 30º respectively. Find the height of the poles and the distance of the point from the poles?

**Ans. 20√3m,20m,60m**

Q.5 The angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6m

Check these stuff as well