Question

if sin A+Sin^2A=1
prove cos^4A+Cos^2A=1​

Answer 1

Answer:

hence proved

Step-by-step explanation:

sin A + sin²A = 1

sinA = 1-sin²A

sin A = cos²A

hence, sin²A = cos⁴A

cos⁴A + cos²A = sin²A + sinA = 1

Answer 2

Given :-

sin A + sin² A = 1

Required To Prove:-

cos⁴ A + cos² A = 1

Proof:-

Given that

sin A + sin² A = 1

=> sin A = 1-sin² A

=> sin A = cos² A ---------(1)

On squaring both sides then

=> sin ² A = cos⁴ A -------(2)

since , sin² A + cos² A = 1

On taking LHS

cos⁴ A + cos² A

=> sin² A + cos² A ----(from (1)&(2))

=> 1

=> RHS

LHS = RHS

Hence, Proved.

Used formulae:-

• sin² A + cos² A = 1