Question

please prove this question and please give correct answer
tomorrow is my maths online test so please give correct answer​

Answer 1

Answer:

ALL THE BEST FOR YOUR MATHS EXAM

Step-by-step explanation:

LHS

cos⁴A -cos²A

(cos²A)²- cos²A

(1-sin²A)²-(1-sin²A)

1+sin⁴A- 2sin²A-1 +sin² A

sin⁴A-sin²A

LHS=RHS

Answer 2

Question : -

Prove that ;

cos⁴ A - cos² A = sin⁴ A - sin² A

ANSWER

Given : -

cos⁴ A - cos² A = sin⁴ A - sin² A

Required to find : -

• LHS = RHS

Solution : -

We can solve this question in 2 methods !

1st method is by solving LHS part and getting the RHS value .

2nd method is by solving the RHS part and getting the LHS value .

So,

Let's have a brief look at both the methods .

1st Method

➔ cos⁴ A - cos² A = sin⁴ A - sin² A

Consider the LHS part

➔ cos⁴ A - cos² A

Taking cos² A common

➔ cos² A ( cos² A - 1 )

From the identity ;

sin² A + cos² A = 1

cos² A = 1 - sin² A

➔ 1 - sin² A ( cos² A - 1 )

➔ 1 ( cos² A - 1 ) - sin² A ( cos² A - 1 )

➔ cos² A - 1 - sin² A cos² A + sin² A

➔ sin² A + cos² A - 1 - sin² A cos² A

since, sin² A + cos² A = 1

➔ 1 - 1 - sin² A cos² A

➔ - sin² A cos² A

Since, we want this in terms of sin let's convert cos² A into sin

Using the identity ;

sin² A + cos² A = 1

cos² A = 1 - sin² A

➔ - sin² A ( 1 - sin² A )

➔ - sin² A + sin⁴ A

➔ sin⁴ A - sin² A

Hence,

➔ LHS = RHS

2nd Method

➔ cos⁴ A - cos² A = sin⁴ A - sin² A

consider the RHS part

➔ sin⁴ A - sin² A

Taking sin² A as common

➔ sin² A ( sin² A - 1 )

From the identity ;

sin² A + cos² A = 1

sin² A = 1 - cos² A

➔ 1 - cos² A ( sin² A - 1 )

➔ 1 ( sin² A - 1 ) - cos² A ( sin² A - 1 )

➔ sin² A - 1 - cos² A sin² A + cos² A

➔ sin² A + cos² A - 1 - cos² A sin² A

Since, sin² A + cos² A = 1

➔ 1 - 1 - cos² A sin² A

➔ - cos² A sin² A

Since, we want this to be in the terms of cos . so, let's convert sin² A into cos A

From the identity ,

sin² A + cos² A = 1

sin² A = 1 - cos² A

➔ - cos² A ( 1 - cos² A )

➔ - cos² A + cos⁴ A

➔ cos⁴ A - cos² A

Hence,

➔ LHS = RHS

➔ Hence Proved ! ✓