In this chapter, we provide RD Sharma Solutions for Class 10 Chapter 5 Trigonometric Ratios Exercise 5.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 10 Chapter 5 Trigonometric Ratios Exercise 5.1 pdf, free RD Sharma Solutions for Class 10 Chapter 5 Trigonometric Ratios Exercise 5.1 book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 5 |

Chapter Name | Trigonometric Ratios |

Exercise | 5.1 |

Category | RD Sharma Solutions |

## RD Sharma Class 10 Solutions Chapter 5 Trigonometric Ratios Exercise 5.1

Question 1.

In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

Solution:

∴ Perpendicular BC – 2 units and

Hypotenuse AC = 3 units

By Phythagoras Theorem, in AABC,

(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2}

AC^{2} = AB^{2} + BC^{2}

⇒ (3)^{2} = (AB)^{2} + (2)^{2}

⇒ 9 = AB^{2} + 4 ⇒ AB^{2} = 9-4 = 5

AB = √5 units

Question 2.

In a ΔABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine

(i) sin A, cos A

(ii) sin C, cos C.

Solution:

Question 3.

In the figure, find tan P and cot R. Is tan P = cot R ?

Solution:

Question 4.

If sin A = (frac { 9 }{ 41 }), compute cos A and tan A.

Solution:

Question 5.

Given 15 cot A = 8, find sin A and sec A.

Solution:

Question 6.

In ΔPQR, right angled at Q, PQ = 4 cm and RQ = 3 cm. Find the values of sin P, sin R, sec P and sec R.

Solution:

Question 7.

If cot 0 = (frac { 7 }{ 8 }), evaluate :

Solution:

Question 8.

If 3 cot A = 4, check whether (frac { 1-{ tan }^{ 2 }A }{ 1+{ tan }^{ 2 }A }) = cos^{2} A – sin^{2} A or not.

Solution:

Question 9.

If tan θ = a/b , Find the Value of (frac { costheta +sintheta }{ costheta -sintheta }).

Solution:

Question 10.

If 3 tan θ = 4, find the value of 4cos θ – sin θ (frac { 4costheta -sintheta }{ 2costheta +sintheta }).

Solution:

Question 11.

If 3 cot 0 = 2, find the value of (frac { 4sinstheta -3costheta }{ 2sintheta +6costheta }).

Solution:

Question 12.

If tan θ = (frac { a }{ b }), prove that

Solution:

Question 13.

If sec θ = (frac { 13 }{ 5 }), show that (frac { 2sinstheta -3costheta }{ 4sintheta -9costheta }) =3.

Solution:

Question 14.

If cos θ (frac { 12 }{ 13 }), show that sin θ (1 – tan θ) (frac { 35 }{ 156 }).

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

If sec θ = (frac { 5 }{ 4 }), find the value of (frac { sinstheta -2costheta }{ tantheta -cottheta }).

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

If tan θ = (frac { 24 }{ 7 }), find that sin θ + cos θ.

Solution:

Question 22.

If sin θ = (frac { a }{ b }), find sec θ + tan θ in terms of a and b.

Solution:

Question 23.

If 8 tan A = 15, find sin A – cos A.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Question 26.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Solution:

∠A and ∠B are acute angles and cos A = cos B

Draw a right angle AABC, in which ∠C – 90°

Question 27.

In a ∆ABC, right angled at A, if tan C =√3 , find the value of sin B cos C + cos B sin C. (C.B.S.E. 2008)

Solution:

Question 28.

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

(i) The value of tan A is always less than 1.

(ii) sec A = (frac { 12 }{ 5 }) for some value of angle A.

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

(iv) cot A is the product of cot and A.

(v) sin θ = (frac { 4 }{ 3 }) for some angle θ.

Solution:

(i) False, value of tan A 0 to infinity.

(ii) True.

(iii) False, cos A is the abbreviation of cosine A.

(iv) False, it is the cotengent of angle A.

(v) Flase, value of sin θ varies on 0 to 1.

Question 29.

Solution:

Question 30.

Solution:

Question 31.

Solution:

Question 32.

If sin θ =(frac { 3 }{ 4 }), prove that

Solution:

Question 33.

Solution:

Question 34.

Solution:

Question 35.

If 3 cos θ-4 sin θ = 2 cos θ + sin θ, find tan θ.

Solution:

Question 36.

If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.

Solution:

∠A and ∠P are acute angles and tan A = tan P Draw a right angled AAPB in which ∠B = 90°

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