solve all the questions and get brainest
9,11,12,14,15,16
I need correct answers
those who give incomplete and incorrect answers I will delete their other answers
So be careful
Answers
Answer:
9. cos2 ∏/8 + cos2 3∏/8 + cos2 5∏/8 + cos2 7∏/8
Let ∏/8 = x then ∏ = 8x
4x = ∏/2 ...(i)
LHS = cos2 ∏/8 + cos2 3∏/8 + cos2 5∏/8 + cos2 7∏/8
= cos2 x + cos2 3x + cos2 5x + cos2 7x
= cos2 x + cos2 3x + cos2 (4x + x) + cos2 (4x + 3x)
= cos2 x + cos2 3x + cos2 (∏/2 + x) + cos2 (∏/2 + 3x) from (i)
= cos2 x + cos2 3x + sin2 x + sin2 3x cos (∏/2 + x) = sin x
= cos2 x + sin2 x + cos2 3x + sin2 3x
= 1 + 1 cos2 x + sin2 x = 1
= 2
= RHS
10. full question not given
11. ( in attachment )
12. I took A instead of x, so in process and final answer take x instead of A ( answer is in attachment)
13. full question not given
14. we have to prove that,
cos³(2x) + 3cos(2x) = 4(cos^6x - sin^6x)
LHS = cos³(2x) + 3cos(2x)
we know, cos2x = 2cos²x - 1
then, cos³(2x) + 3cos(2x) = (2cos²x - 1)³ + 3(2cos²x - 1)
= (2cos²x)³ - 3(2cos²x)² + 3(2cos²x).1² - 1 + 6cos²x - 3
= 8cos^6x - 12cos⁴x + 6cos²x + 6cos²x - 4
= 8cos^6x - 12cos⁴x + 12cos²x - 4
= 8cos^6x - 12cos²x(cos²x - 1) - 4
= 8cos^6x - 12(1 - sin²x) sin²x - 4
= 4cos^6x + 4cos^6x - 12sin²x + 12sin⁴x - 4
= 4cos^6x + 4(1 - sin²x)³ - 12sin²x + 12sin⁴x - 4
= 4cos^6x + 4(1 - 3sin⁴x + 3sin²x - sin^6x) - 12sin²x + 12sin⁴x - 4
= 4cos^6x + 4 - 12sin⁴x + 12sin²x - 4sin^6x - 12sin²x + 12sin⁴x - 4
= 4cos^6x - 4sin^6x
= 4(cos^6x - sin^6x) = RHS
15. ( in attachment)
16. ( in attachment)
hope these helps u...mate ...BTS ARMY ✌✌
