Question

sin⁴theta - cos⁴ theta/ sin² theta - cos²theta​

Answer 1

Answer:

A=sin2θ+cos4θ

    =sin2θ+cos2θ.cos2θ

    =sin2θ+cos2θ(1−sin2θ)

    =sin2θ+cos2θ−sin2θcos2θ

    =1−41(2sinθcosθ)2

    =1−41sin22θ

Min.(sin22θ)=0

Max.(sin22θ)=1

Min.(A)=1−41.Max(sin22θ)

=1−41.1=43

Max.(A)=1−41.Min.(sin22

Ans 3 upon 4 < A < 1

Answer 2

Answer:

1

Step-by-step explanation:

Firstly,

sin⁴theta - cos⁴ theta = (sin² theta - cos²theta) (sin² theta + cos²theta)

[ a²-b² = (a+b) (a-b)]

Thus, sin² theta - cos²theta, gets cancelled out from numberator and denominator.

=> The given expression is now equal to sin² theta + cos²theta

Since, according to identity, sin² theta + cos²theta= 1

Hence, answer is 1.

I hope you got the answer!