# HSSlive: Plus One & Plus Two Notes & Solutions for Kerala State Board

## AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 11 Trigonometry Ex 11.4 Book Answers AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.4 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 11 Trigonometry Ex 11.4 Book Answers

## Andhra Pradesh State Board Class 10th Maths Chapter 11 Trigonometry Ex 11.4 Books Solutions

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## AP Board Class 10th Maths Chapter 11 Trigonometry Ex 11.4 Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 10th Maths Chapter 11 Trigonometry Ex 11.4 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

### 10th Class Maths 11th Lesson Trigonometry Ex 11.4 Textbook Questions and Answers

Question 1.
Evaluate the following:
i) (1 + tan θ + sec θ) (1 + cot θ – cosec θ)
Given (1 + tan θ + sec θ) (1 + cot θ – cosec θ) ii) (sin θ + cos θ)2 + (sin θ – cos θ)2
Given (sin θ + cos θ)2 + (sin θ – cos θ)2
= (sin2 θ + cos2 θ + 2 sin θ cos θ) + (sin2 θ + cos2 θ – 2 sin θ cos θ) [∵ (a + b)2 = a2 + b2 + 2ab
(a – b)2 = a2 + b2 – 2ab]
= 1 + 2 sin θ cos θ + 1 – 2 sin θ cos θ [∵ sin2 θ + cos2 θ = 1]
= 1 + 1
= 2

iii) (sec2 θ – 1) (cosec2 θ – 1)
Given (sec2 θ – 1) (cosec2 θ – 1)
= tan2 θ × cot2 θ [∵ sec2 θ – tan2 θ = 1; cosec2 θ – cot2 θ = 1]
= tan2 θ × 1tan2𝜃 = 1

Question 2.
Show that (cosec θ – cot θ)2 = 1−cos𝜃1+cos𝜃 Question 3.
Show that 1+sin𝐴1−sin𝐴‾‾‾‾‾‾√ = sec A + tan A
Given that L.H.S. = 1+sin𝐴1−sin𝐴‾‾‾‾‾‾√
Rationalise the denominator, rational factor of 1 – sin A is 1 + sin A. [∵ (a + b)(a + b) = (a + b)2]; (a – b)(a + b) = a2 — b2]
= (1+sin𝐴)2cos2𝐴‾‾‾‾‾‾‾‾√
= 1+sin𝐴cos𝐴
= 1cos𝐴+sin𝐴cos𝐴
= sec A + tan A = R.H.S.

Question 4.
Show that 1−tan2𝐴cot2𝐴−1 = tan2 A Question 5.
Show that 1cos𝜃 – cos θ = tan θ – sin θ. Question 6.
Simplify sec A (1 – sin A) (sec A + tan A)
L.H.S. = sec A (1 – sin A) (sec A + tan A)
= (sec A – sec A . sin A) (sec A + tan A)
= (sec A – 1cos𝐴 . sin A) (sec A + tan A)
= (sec A – tan A) (sec A + tan A)
= sec2 A – tan2 A [∵ sec2 A – tan2 A = 1]
= 1

Question 7.
Prove that (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2 A + cot2 A
L.H.S. = (sin A + cosec A)2 + (cos A + sec A)2
= (sin2 A + cosec2 A + 2 sin A . cosec A) + (cos2 A – sec2 A + 2 cos A . sec A) [∵ (a + b)2 = a2 + b2 + 2ab]
= (sin2 A + cos2 A) + cosec2 A + 2 sin A . 1sin𝐴 + sec2 A + 2 cos A . 1cos𝐴
[∵ 1sin𝐴 = cosec A; 1cos𝐴 = sec A]
= 1 +(1 + cot2 A) + 2 + (1 + tan2 A) + 2
[∵ sin2 A + cos2 A = 1; cosec2 A = 1 + cot2 A; sec2 A = 1 + tan2 A]
= 7 + tan2 A + cot2 A
= R.H.S.

Question 8.
Simplify (1 – cos θ) (1 + cos θ) (1 + cot2 θ)
Given that
(1 – cos θ) (1 + cos θ) (1 + cot2 θ)
= (1 – cos2 θ) (1 + cot2 θ)
[∵ (a – b) (a + b) = a2 – b2]
= sin2 θ. cosec2 θ [∵ 1 – cos2 θ = sin2 θ; 1 + cot2 θ = cosec2 θ]
= sin2 θ . 1sin2𝜃 [∵ cosec θ = 1sin𝜃]
= 1

Question 9.
If sec θ + tan θ = p, then what is the value of sec θ – tan θ?
Given that sec θ + tan θ = p ,
We know that sec2 θ – tan2 θ = 1
sec2 θ – tan2 θ = (sec θ + tan θ) (sec θ – tan θ)
= p (sec θ – tan θ)
= 1 (from given)
⇒ sec θ – tan θ = 1𝑝

Question 10.
If cosec θ + cot θ = k, then prove that cos θ = 𝑘2−1𝑘2+1
Method-I:
Given that cosec θ + cot θ = k
R.H.S. = 𝑘2−1𝑘2+1 Method – II:
Given that cosec θ + cot θ = k ……..(1)
We know that cosec2 θ – cot2 θ = 1
⇒ (cosec θ + cot θ) (cosec θ – cot θ) = 1 [∵ a2 – b2 = (a -b)(a + b)]
⇒ k (cosec θ – cot θ) = 1
⇒ (cosec θ – cot θ) = 1𝑘
By solving (1) and (2) According to identity cos2 θ + sin2 θ = 1 Hence proved.

## Andhra Pradesh Board Class 10th Maths Chapter 11 Trigonometry Ex 11.4 Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 11 Trigonometry Ex 11.4 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 11 Trigonometry Ex 11.4 exam preparation. The AP Board STD 10th Maths Chapter 11 Trigonometry Ex 11.4 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 11 Trigonometry Ex 11.4 Books State Board syllabus with maximum efficiency.

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