Question

if sinø + sin²ø = 1 then show that cos²ø + cos⁴ø = 1​

Answer 1

$\huge\red{\boxed{\huge\blue{\boxed{\orange{\mathfrak{ANSWER}}}}}}$

sin∅ + sin²∅ = 1

sin∅ = 1 - sin²

sin∅ = cos²∅ [sin²∅ + cos²∅ = 1, cos²∅ = 1-sin²∅]

squaring on both side

sin²∅ = cos⁴∅ .... (1)

cos²∅ + cos⁴∅ = 1

L.H.S.

= cos² + cos⁴∅

= cos² + sin²∅ .....from (1)

= sin²∅ + cos²∅

= 1 [ sin²∅ + cos²∅ = 1 ]

= R.H.S.

L.H.S. = R.H.S.

hence proved