Question

What is the period of 3sin²x+5cos²x

Answer 1

we have to find extreme value of 3sin²x + 5cos²x

3sin²x + 5cos²x

= 3sin²x + 3cos²x + 2cos²x

= 3(sin²x + cos²x) + 2cos²x

we know,

so, sin²x + cos²x = 1

now, 3(sin²x + cos²x) + 2cos²x = 3 × 1 + 2cos²x

= 3 + 2cos²x

cosine function lies between -1 to 1

e.g., - 1 ≤ cosx ≤ 1

or, 0 ≤ cos²x ≤ 1

now, 0 × 2 ≤ 2cos²x ≤ 2 × 1

0 ≤ 2cos²x ≤ 2

0 + 3 ≤ 3 + 2cos²x ≤ 3 + 2

3 ≤ 3 + 2cos²x ≤ 5

hence, maximum or extreme value of 3sin²x + 5cos²x = 5

Answer 2

Step-by-step explanation:

maximum value =+5

minimum =-5