How do you simplify the expression 1-sec-2x- - Maths Q-A

Simplify the given expressionWe know the identity sec^2x tan^2x=1⇒ 1+tan^2x=sec^2x⇒1 sec^2x= tan^2x Hence, the required answer is 1 sec^2x= tan^2x ...

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Standard XII

Mathematics

Derivative of Standard Inverse Trigonometric Functions

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Question

How do you simplify the expression $1 - s e c^{2} x$ ?

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Solution

Simplify the given expression
We know the identity $s e c^{2} x - \tan^{2} x = 1$
$\Rightarrow 1 + \tan^{2} x = s e c^{2} x$
$\Rightarrow$ $1 - s e c^{2} x = - \tan^{2} x$
Hence, the required answer is $1 - s e c^{2} x = - \tan^{2} x$

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How do you simplify the expression 1-sec2x?

Simplify the given expressionWe know the identity sec2x-tan2x=1⇒1+tan2x=sec2x⇒1-sec2x=-tan2x Hence, the required answer is 1-sec2x=-tan2x

How do you simplify the expression $1 - s e c^{2} x$ ?

Simplify the given expression
We know the identity $s e c^{2} x - \tan^{2} x = 1$
$\Rightarrow 1 + \tan^{2} x = s e c^{2} x$
$\Rightarrow$ $1 - s e c^{2} x = - \tan^{2} x$
Hence, the required answer is $1 - s e c^{2} x = - \tan^{2} x$