Question

cos^4x/cos^2y+sin^4x/sin^2y=1 then prove cos^4y/cos^2x+sin^4y/sin^2x=1

Answer 1

Answer:

Step-by-step explanation:

Cos^4x/cos^2y+sin^4x/sin^2y=1 then prove cos^4y/cos^2x+sin^4y/sin^2x=1

Cos⁴x/Cos²y  + Sin⁴x/Sin²y = 1

=> Cos⁴xSin²y  + Sin⁴xCos²y = Cos²ySin²y

=> Cos⁴xSin²y + (1 - Cos²x)²Cos²y = Cos²ySin²y

=>  Cos⁴xSin²y + (1 + Cos⁴x  -2Cos²x )Cos²y = Cos²ySin²y

=> Cos⁴xSin²y  + Cos⁴xCos²y  + Cos²y - 2Cos²xCos²y = Cos²ySin²y

=>  Cos⁴x(Sin²y + Cos²y ) + Cos²y(1 - Sin²y)   - 2Cos²xCos²y = 0

=> Cos⁴x + Cos⁴y   - 2Cos²xCos²y = 0

=> (Cos²x - Cos²y)² = 0

=> Cos²x = Cos²y

=> Sin²x = Sin²y

Using this value in

Cos⁴y/Cos²x  + Sin⁴y/Sin²x = 1

LHS = Cos⁴y/ Cos²y + Sin⁴y/Sin²y

= Cos²y + Sin²y

= 1

= RHS