Math, asked by kukuupreti, 2 months ago

sin^4 A-cos^4 A=2sin^2A-1
prove the following identity ​

Answers

Answered by sahakuntal2005
1

Answer:

Step-by-step explanation:

Given:

I−sin  

4

A−cos  

4

A;II−2sin  

2

A−1;III=1−2cos  

2

A;IV−sin  

2

A−cos  

2

A

Taking I term

=sin  

4

A−cos  

4

A=(sin  

2

A)  

2

−(cos  

2

A)  

2

=(sin  

2

A−cos  

2

A)(sin  

2

A+cos  

2

A)[∵(a  

2

−b  

2

)=(a+b)(a−b)]

=(sin  

2

A−cos  

2

A)(1)[∵cos  

2

θ+sin  

2

θ=1]=(sin  

2

A−cos  

2

A)...(1)→IV term

From Eq (1)

=[sin  

2

A−(1−sin  

2

A)]=sin  

2

A−1+sin  

2

A=2sin  

2

A−1→II term

again from Eq (1)

=[(1−cos  

2

A)−cos  

2

A][∵cos  

2

θ+sin  

2

θ=1]=1−2cos  

2

A→III term

Hence, I=II=III=IV

Hence proved

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