06 Apr 2022

Samacheer kalvi 10th Maths – Trigonometry Ex 6.1

10th Maths Book Back Question and Answers – Chapter 6 Exercise 6.1:

Samacheer Kalvi 10th Standard Maths Book Back Questions with Answers PDF uploaded and the same given below. Class-tenth candidates and those preparing for TNPSC exams can check the Maths Book Back Answers PDF below. Samacheer Kalvi Class 10th Std Maths Book Back Answers Chapter 6 Trigonometry Exercise 6.1 Solutions are available below. Check the complete Samacheer Kalvi 10th Maths – Trigonometry Ex 6.1 Book Back Answers below:

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Samacheer Kalvi 10th Maths Book Back Answers – Ex 6.1 Trigonometry

Samacheer Kalvi 10th Maths Book Subject One Mark, Two Mark, Five Mark Guide questions and answers are below. Check Maths Book Back Questions with Answers. Take the printout and use it for exam purposes.

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Chapter 6

Exercise 6.1 Trigonometry

1. Prove the following identities.
(i) cot θ + tan θ = sec θ cosec θ
(ii) tan4θ + tan2θ = sec4θ – sec2θ
Solution:
10th maths unit - 6 book back question with answer

2. Prove the following identities
10th maths unit - 6 book back questions with answer

Solution:

10th maths unit - 6 book back questions with answer

3. Prove the following identities
10th maths unit - 6 book back questions with answer

Solution:

10th maths unit - 6 book back questions with answer

4. Prove the following identities
(i) sec6θ = tan6θ + 3tan2θ sec2θ + 1
(ii) (sinθ + secθ)2 + (cosθ + cosecθ)2= 1 + (secθ + cosecθ)2
Solu:

(i) L.H.S = sec6θ = (sec2θ)3 = (1 + tan2θ )3 = (tan2θ + 1)3
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= (tan2θ)3 + 3(tan2θ)2 × 1 + 3 × tan2θ × 12 + 1
= tan6θ + 3tan2θ × (sec2θ – 1) + 3tan2θ + 1
= tan6θ + 3tan2θsec2θ – 3tan2θ + 3tan2θ +1
= tan6θ + 3tan2θ sec2θ + 1 = R.H.S

(ii) L.H.S = (sinθ + secθ )2 + (cosθ + cosecθ)2
= sin2θ + 2sinθ secθ + sec2θ + cos2θ + 2cosθ cosecθ+ cosec2θ
10th maths unit - 6 book back questions with answer




5. Prove the following identities
10th maths unit - 6 book back questions with answer

Solution:

10th maths unit - 6 book back questions with answer

(ii)

10th maths unit - 6 book back questions with answer

6. Prove the following identities
10th maths unit - 6 book back questions with answer

10th maths unit - 6 book back questions with answer

7.

10th maths unit - 6 book back questions with answer

Solution:

10th maths unit - 6 book back questions with answer

8.

10th maths unit - 6 book back questions with answer

Solution:
(i) LHS:
10th unit - 6 book back questions with answer

10th maths unit - 6 book back questions with answer

10th maths unit - 6 book back questions with answer

9. (i) If sinθ + cosθ = p and secθ + cosecθ = q then prove that q(p2 – 1) = 2p
(ii) If sinθ(1 + sin2θ) = cos2θ, then prove that cos6θ – 4cos4θ + 8cos2θ = 4
Solution:

10th maths unit - 6 book back questions with answer

(ii) Given sinθ(1 + sin2θ) = cos2θ
Substitute sin2θ = 1 – cos2θ and take cos θ = c
squaring (1) on both sides we get
sin2θ(1 + sin2θ)= cos4θ
(1 – c2)(1 + 1 – c2) = c4
(1 – c2)(2 – c2)= c4
(1 – c2)(4 + c4– 4c2) = c4
4 + c4– 4c– 4c2 – c6 + 4c4 = c4
 -c6 + 4c4 – 8c2 = -4
c– 4c4 + 8c2 = -4
ie cos 6θ – 4cos 4θ + 8cos2θ = 4 = RHS
∴ Hence proved

10.

10th maths unit - 6 book back questions with answer

Other Important Links for 10th Maths Book Back Answers Solutions:

For the 10th Maths Chapter 6 book back question and answers, check the link – Samacheer kalvi 10th Maths Chapter 6 Coordinate Geometry

Click here for the complete Samacheer Kalvi 10th Maths Book Back Solution Guide PDF – 10th Maths Book Back Answers




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