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**RS Aggarwal Class 10 Solutions Chapter 8 Trigonometric Ratios of Complementary Angles**

**Exercise 8**

**Question 1:**

**Question 2:**

(i) _{ }

∴ LHS = RHS

(ii) _{ }

∴ LHS = RHS

(iii) _{ }

∴ LHS = RHS

(iv) _{ }

∴ LHS = RHS

(v)

∴ LHS = RHS

**Question 3:**

(i)

(ii)

(iii)

(iv)

**Question 4:**

(i) LHS = cos81° – sin9°

= cos(90° -9°)- sin9° = sin9° – sin9°

= 0 = RHS

(ii) LHS = tan71° – cot19°

=tan(90° – 19°) – cot19° =cot19° – cot19°

=0 = RHS

(iii) LHS = cosec80° – sec10°

= cosec(90° – 10°) – sec(10°)

= sec10° – sec10° = 0

= RHS

**Question 5:**

(i) LHS = sin53° cos37° + cos53° sin37°

∴ LHS = RHS

(ii) LHS = cos54° cos36° + sin54° sin36°

∴ LHS = RHS

(iii) LHS = sec70° sin20° + cos20° cosec70°

∴ LHS = RHS

**Question 6:**

(i) _{ }

∴ LHS = RHS

(ii) _{ }

∴ LHS = RHS

(iii) _{ }

∴ LHS = RHS

(iv) _{ }LHS = cot10°cot20° cot60°cot70° cot°

∴ LHS = RHS

(v) cosec15°cosec355°cosec55°cosec60°cosec75°

∴ LHS = RHS

**Question 7:**

(i) LHS=

= RHS

(ii) LHS=

= RHS

(iii) LHS=

= RHS

(iv) LHS = cosec(65° + θ) – sec(25°- θ) – tan(55° – θ) + cot(35° + θ)

= RHS

(v) LHS =

= 0 + 1 = 1

= RHS

**Question 8:**

**Question 9:**

**Question 10:**

**Question 11:**

**Question 12:**

**Question 13:**

**Question 14:**

**Question 15:**

**Question 16:**

**Question 17:**

**Question 18:**

**Question 19:**

**Question 20:**

**Question 21:**

**Question 22:**

**Question 23:**

**Question 24:**

**Question 25:**

**Question 26:**

**Question 27:**

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