subikaacharya
Answered

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tan^2A -sin^2A=sin^2a Tan^2A​

Sagot :

Answer:

see explanation

Step-by-step explanation:

Using the identity

sin²A = 1 - cos²A , tanA = [tex]\frac{sinA}{cosA}[/tex]

Consider the left side

tan²A - sin²A

= [tex]\frac{sin^2A}{cos^2A}[/tex] - sin²A

[tex]\frac{sin^2A-sin^2Acos^2A}{cos^2A}[/tex]

= [tex]\frac{sin^2A(1-cos^2A)}{cos^2A}[/tex]

= [tex]\frac{sin^2A.sin^2A}{cos^2A}[/tex]

= sin²A × [tex]\frac{sin^2A}{cos^2A}[/tex]

= sin²A . tan²A

= right side , thus verified

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