Question

if sinA+sin2A+sin3A=1 prove that - cos6A-4cos4A+8cos2A=4

Answer 1

Answer:

cos^6A - 4 cos^4A + 8cos^2A = 4

Step-by-step explanation:

Please find the answer

sinA + sin²A + sin³A = 1

sinA + sin³A = 1 - sin²A = cos²A

sinA(1+sin²A) = cos²A

sinA(2 -cos²A) = cos²A

Squaring both sides,

sin²A(4-4cos²A +cos^4A) = cos^4A

(1-cos²A)(4-4cos²A +cos^4A) = cos^4A

4-4cos²A +cos^4A-4cos²A+4cos^A-cos^6A = cos^4A

4 -cos^6A +4cos^4A -8cos^2A = 0

cos^6A - 4 cos^4A + 8cos^2A = 4