Question

Please answer the question if you answer I will mark u in brain list

Answer 1

Solution :-

Solving LHS,

→ √[2 + √{2+√(2+2cos4A)}]

→ √[2 + √{2+√2(1+cos4A)}]

→ √[2 + √{2+√2(1 + cos2(2A)}]

Putting cos2x = 2cos²x - 1

→ √[2 + √{2+√2( 1 + 2cos²2A - 1)

→ √[2 + √(2+√4cos²2A)]

→ √[2 + √(2+2cos2A)]

→ √[2 + √{2+2(2cos²A-1)}]

→ √[2 + √(2+4cos²A-2)]

→ √(2 + 2cosA)

→ √2(1 + cosA)

→ √2( 1 + {2cos²(A/2) - 1})

→ √( 2 + 4cos²(A/2) - 2)

→ √(4cos²(A/2))

→ 2cos(A/2)

→ RHS (Proved).