Question

Sec²∅ - tan²∅ = ? ............

Answer 1

Sin²∅ - tan²∅ = 1 ............

Step-by-step explanation:

Answer 2

The correct answer is 1.

Given: The equation = $Sec^{2}$∅ - $tan^{2}$∅.

To Find: Evaluate the equation.

Solution:

As we know that  $Sec^{2}$∅ - $tan^{2}$∅ is an identity.

$Sec^{2}$∅ - $tan^{2}$∅ = 1.

Proof of identity

$Sec^{2}$x - $tan^{2}$x

= $\frac{1}{cos^{2} x} -\frac{sin^{2}x }{cos^{2} x}$

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

As we know the identity $sin^{2} x+cos^{2}x=1$.

$1-sin^{2} x=cos^{2}x$

Now put the value $1-sin^{2} x=cos^{2}x$ in equation 1.

= $\frac{cos^{2} x}{cos^{2} x}$

$Sec^{2}$x - $tan^{2}$x = 1

Hence, the value of  $Sec^{2}$x - $tan^{2}$x is 1.

#SPJ2