Question

Salute u if u solved this
(Trigonometric ratios of multiple angles )
MATH LEGENDS CAN SOLVE THIS EASILY (question for math leaders)

Answer 1

Answer:

Cos4A = 8Sin⁴A - 8Sin²A + 1

Step-by-step explanation:

to be proved

Cos4A = 8Sin⁴A - 8Sin²A + 1

LHS =Cos4A

using  Cos2θ = Cos²θ - Sin²θ = 2Cos²θ - 1 = 1 - 2Sin²θ

Cos4A = (2Cos²2A - 1)

Cos2A =( 1 - 2Sin²A)

=>

LHS

= 2( 1 - 2Sin²A)² - 1

= 2( 1 + 4Sin⁴A - 4Sin²A) - 1

= 8Sin⁴A - 8Sin²A + 2 - 1

= 8Sin⁴A - 8Sin²A + 1

= RHS

QED

Hence proved that

Cos4A = 8Sin⁴A - 8Sin²A + 1