Question 1

Question 1: If sin θ = , find the values of cos θ and tan θ.

Accepted Answer

sin θ = … [Given] We know that, sin2 θ + cos2 θ = 1 …[Taking square root of both sides] Now, tan θ = Alternate Method: sin θ = …(i) [Given] Consider ∆ABC, where ∠ABC 90° and ∠ACB = θ. sin θ = … (ii) [By definition] ∴ = … [From (i) and (ii)] LetAB = 7k and AC = 25k In ∆ABC, ∠B = 90° ∴ AB2 + BC2 = AC2

Question 2

Question 2: If tan θ = , find the values of sec θ and cos θ.

Accepted Answer

Alternate Method: tan θ = …(i)[Given] Consider ∆ABC, where ∠ABC 90° and ∠ACB = θ. tan θ = … (ii) [By definition] ∴ = … [From (i) and (ii)] Let AB = 3k and BC 4k In ∆ABC,∠B = 90° ∴ AB2 + BC2 = AC2 …[Pythagoras theorem] ∴ (3k)2 + (4k)2 = AC2 ∴ 9k2 + 16k2 = AC2 ∴ AC2 = 25k2 ∴ AC = 5k …[Taking square ro

Question 3

Question 3: If cot θ = , find the values of cosec θ and sin θ

Accepted Answer

..[Taking square root of both sides] Alternate Method: cot θ = ….(i) [Given] Consider ∆ABC, where ∠ABC = 90° and ∠ACB = θ cot θ = …(ii) [By defnition] ∴ = ….. [From (i) and (ii)] Let BC = 40k and AB = 9k In ∆ABC, ∠B = 90° ∴ AB2 + BC2 = AC2 … [Pythagoras theorem] ∴ (9k)2 + (40k)2 = AC2 ∴ 81k2 + 1600k

Question 4

Question 4: If 5 sec θ – 12 cosec θ = θ, find the values of sec θ, cos θ and sin θ.

Accepted Answer

5 sec θ – 12 cosec θ = 0 …[Given] ∴ 5 sec θ = 12 cosec θ

Question 5

Question 5: If tan θ = 1, then find the value of

Accepted Answer

tan θ = 1 … [Given] We know that, tan 45° = 1 ∴ tan θ = tan 45° ∴ θ = 45°

Question 6

Question 6: Prove that: i. ii. cos2 θ (1+ tan2 θ) = 1 iii. iv. (sec θ – cos θ) (cot θ + tan θ) tan θ. sec θ v. cot θ + tan θ cosec θ. sec θ vi. vii. sin4 θ – cos4 θ = 1 – 2 cos2 θ viii. Proof:

Accepted Answer

Step-by-step solution provided.

Question 7

Question 2: Complete the relations in ratios given below. (Textbook pg, no. 124)

Accepted Answer

i. = [tan θ] ii. sin θ = cos (90 – θ) iii. cos θ = (90 – θ) iv. tan θ × tan (90 – θ) = 1

Question 8

Question 3: Complete the equation. (Textbook pg. no, 124) sin2 θ + cos2 θ = [______]

Accepted Answer

sin2 θ + cos2 θ = [1]

Question 9

Question 4: Write the values of the following trigonometric ratios. (Textbook pg. no. 124)

Accepted Answer

Step-by-step solution provided.

Question 10

Question 1: Fill in the blanks with reference to the figure given below. (Textbook pg. no. 124)

Accepted Answer

block bg-white dark:bg-slate-900/80 border-l-4 border-emerald-500 rounded-r-xl p-5 my-3 shadow-xs border border-slate-200/60 dark:border-slate-800"> Solution & Step-by-Step Answer: Question 2 Maharashtra Board Solution Complete the relations in ratios given below. (Textbook pg, no. 124) Solution & S

Chapter 6 Trigonometry Practice Set 6.1 Solutions