Question

if sin x + sin²x+ sin³x= 1 then prove that cos⁶x - 4cos⁴x+ 8 cos²x=4.​

Answer 1

Answer:

Step-by-step explanation:

Hey mate here is your answer:

⇒sin x + sin²x+sin³x=1,

⇒sin x + sin³x=1-sin²x,

⇒(sin x + sin³x)²=(1-sin²x)²,

⇒sin²x+sin^6 x+2 sin^4 x=cos^4 x,

⇒1-cos²x+(1-cos²x)³+2(1-cos²x)²=cos^4 x,

⇒1-cos²x+1-3 cos²x+3 cos^4 x-cos^6 x+2-4cos²x+2 cos^4 x=cos^4 x,

Hence it is proved that,cos⁶x - 4cos⁴x+ 8 cos²x=4.​

Hope it helps you.