# NCERT Solutions For Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 8 |

Exercise | Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.4 |

Number of Questions Solved | 5 |

## NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

**NCERT TEXTBOOK EXERCISES**

**Question 1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.**

**Solution:**

From trigonometric identity, cosecÂ² A â€“ cotÂ² A = 1, we get

**Question 2. Write all the other trigonometric ratios of âˆ A in terms of sec A.**

**Solution:**

Since sinÂ² A + cosÂ² A = 1, therefore

**Question 3. Evaluate:**

(I)

(ii) sin 25Â° cos 65Â° + cos 25Â° sin 65Â°

**Solution:**

(ii) sin 25Â° cos 65Â° + cos 25Â° sin 65Â° = sin 25Â° cos (90Â° â€“ 25Â°) + cos 25Â° sin (90Â° â€“ 25Â°)

= sin 25Â° sin 25Â° + cos 25Â° cos 25Â°

= sinÂ² 25Â° + cosÂ² 25Â° = 1

**Question 4. Choose the correct option. Justify your choice.**

(i) 9 secÂ² A â€“ 9 tanÂ² A =

(A) 1

(B) 9

(C) 8

(D) 0

(ii) (1 + tan Î¸ + sec Î¸) (1 + cot Î¸ â€“ cosec Î¸ ) =

(A) 0

(B) 1

(C) 2

(D) -1

(iii) (sec A + tan A) (1 â€“ sin A) =

(A) sec A

(B) sin A

(C) cosec A

(D) cos A

(iv)Â 1+tan2A1+cot2A

(A) secÂ² A

(B) -1

(C) cotÂ² A

(D) tanÂ² A

**Solution:**

(i) 9 secÂ² A â€“ 9 tanÂ² A = 9(secÂ² A â€“ tanÂ² A) = 9 x 1 = 9

Correct option is (B)

**Question 5. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.**

**Solution:**

## NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.4 PDF

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