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

Step-by-step explanation:

LHS

cos⁴A-cos²A

(cos²A)² - cos²A [cos²A=1-sin²A]

(1-sin²A)²- 1+sin² A

1+sin⁴A-2sin²A-1+sin²A

sin⁴ A -sin²A

LHS=RHS

Answer 2

GIVEN :

Cos⁴A - Cos²A = Sin⁴A - Sin²A

TO PROVE :

LHS = RHS

Where ,

LHS = Cos⁴A - Cos²A

RHS = Sin⁴A - Sin²A

CONCEPT USED :

$Sin²A = 1 - Cos²A$

$Cos²A = 1 - Sin²A$

PROOF :

$LHS = Cos⁴A - Cos²A$

taking out Cos²A as common :-

$= > Cos²A \: (Cos²A - 1)$

$= > - Cos²A(1 - Cos²A)$

$= > we \: know \: Sin²A = 1 - Cos²A$

$= > - Cos²A \: Sin²A$

$= >LHS \: = - Cos²A \: Sin²A$

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Now ,

$RHS = Sin⁴A - Sin²A$

taking out Sin²A as common :-

$= > Sin²A( Sin²A - 1)$

$= > - Sin²A(1 - Sin²A)$

$= > we \: know \: Cos²A = 1 - Sin²A$

$= > - Sin²ACos²A$

$= >RHS = - Sin²ACos²A$

$LHS = RHS = - Sin²ACos²A$

hence proved LHS = RHS

__________________________

Some trigonometry identities :-

1. Sin²x + Cos²x = 1

2. Cossec²x-cot²x =1

3.Sec²x -tan²x=1