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**HOTS QUESTIONS**

**Q1. What is the maximum value of **

**Hint:** âˆµ = 3 sin Î¸

Since maximum value of â€˜sin Î¸â€™ is 1

âˆ´ maximum value of 3 sin Î¸ is 3 Ã— 1 i.e. 3

â‡’ maximum value of is 3.

**Q2. If sin Î¸ = 1/3, then find the value of 9 cot ^{2}Î¸ + 9.**

**Hint: **cot^{2} Î¸ = cosec^{2} Î¸ â€“ 1

âˆ´ 9 cot^{2}Î¸ + 9 = 9(8) + 9 = 72 + 9 = 81

**Q3. If 4 tan Î¸ = 3, then find the value of **

**Hint:**

**Q4. If sin Î± = 1/2 and cos Î² = 1/2 then find the value of (Î± + Î²).**

**Hint:**

**Q5. If sin Î¸ + cos Î¸ = âˆš3 , find the value of tan Î¸ + cot Î¸ .**

**Hint: **sin Î¸ + cos Î¸ = **âˆš**3 â‡’ (sin Î¸ + cos Î¸)^{2} = 3

â‡’ sin^{2} Î¸ + cos^{2} Î¸ + 2 sin Î¸ . cos Î¸ = 3

â‡’ 1 + 2 sin Î¸ . cos Î¸ = 3 â‡’ 2 sin Î¸ . cos Î¸ = 2 [âˆ´ sin^{2}Î¸ + cos^{2}Î¸ = 1]

â‡’ sin Î¸ . cos Î¸ =1 â‡’ 1 =

â‡’

Thus, tanÎ¸ + cotÎ¸ = 1

**Q6. cos (A+B) = 1/2 and sin (Aâ€“B) = 1/2 ; 0Â° < (A + B) < 90Â° and (A â€“ B) > 0Â°. What are the values of âˆ A and âˆ B?**

**Hint:**

...(1)

...(2)

Adding (1) and (2), 2A = 90 â‡’ A = 45

From (1) 45Â° + B = 60Â° â‡’ B = 60Â° â€“ 45Â° = 15Â°

Thus, âˆ A = 45Â° and âˆ B = 15Â°

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