Respuesta :
Answer:
The basic identity used is [tex]\bold{\sin ^{2} x+\cos ^{2} x=1}[/tex].
Solution:
In this problem some of the basic trigonometric identities are used to prove the given expression.
Let’s first take the LHS:
[tex]\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}[/tex]
Step one:
The sum of squares of Sine and Cosine is 1 which is:
[tex]\sin ^{2} x+\cos ^{2} x=1[/tex]
On substituting the above identity in the given expression, we get,
[tex]\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\frac{1}{\cos x} \rightarrow(1)[/tex]
Step two:
The reciprocal of cosine is secant which is:
[tex]\cos x=\frac{1}{\sec x}[/tex]
On substituting the above identity in equation (1), we get,
[tex]\Rightarrow \frac{\sin ^{2} x+\cos ^{2} x}{\cos x}=\sec x[/tex]
Thus, RHS is obtained.
Using the identity [tex]\sin ^{2} x+\cos ^{2} x=1[/tex], the given expression is verified.
