Question

tan^2A-sec^2A is equal to?​

Answer 1

Answer:

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-1

tan^2+1=sec^2.

tan^2-sec^2=-1

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Answer 2

Answer :

tan²A - sec²A

We know that

tan²A = sin²A/cos²A

sec²A = 1/cos²A

Now , substitute

$( \frac{ {\sin}^{2}a }{ {\cos}^{2} a} ) - ( \frac{1}{ { \cos}^{2}a } ) \\ \\ = \frac{ { \sin}^{2}a - 1 }{ { \cos}^{2}a }$

Taking common -1

$= \dfrac{ - 1(1 - { \sin}^{2}a) }{ { \cos}^{2} a }$

Using

cos²A = 1 - sin²A

$= \frac{ - { \cos}^{2} a}{ { \cos}^{2}a } \\ \\ = - 1$

Used concepts

$\to{\sf{trigonometric \: \: ratios}} \\ \to { \sf{trigonometric \: \: identities \: }}$