If f(x) = cos^2 x + sec^2 x,then its value is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the function $f(x) = \cos^2 x + \sec^2 x$.We can rewrite the expression by completing the square:$f(x) = (\cos x - \sec x)^2 + 2 \cos x \sec

Vedclass · Accepted Answer

$f(x) \geq 2$

Vedclass · Answer

(D) Given the function $f(x) = \cos^2 x + \sec^2 x$.We can rewrite the expression by completing the square:$f(x) = (\cos x - \sec x)^2 + 2 \cos x \sec x$Since $\cos x \cdot \sec x = 1$,the expression becomes:$f(x) = (\cos x - \sec x)^2 + 2(1)$$f(x) = (\cos x - \sec x)^2 + 2$Since the square of any real number is always non-negative,i.e.,$(\cos x - \sec x)^2 \geq 0$,it follows that:$f(x) \geq 0 + 2$$f(x) \geq 2$Therefore,the value of the function is always greater than or equal to $2$.

If $f(x) = \cos^2 x + \sec^2 x$,then its value is always:

Similar Questions

If $\sin \theta + \cos \theta = 1$,then $\sin \theta \cos \theta = $

If $\log_a b + \log_b c + \log_c a$ vanishes,where $a, b,$ and $c$ are positive real numbers different from unity,then the value of $(\log_a b)^3 + (\log_b c)^3 + (\log_c a)^3$ is

If $7 \sin a = 24 \cos a$,then the value of $14 \tan a - 75 \cos a - 7 \sec a$ is equal to:

If $5 \sin \theta = 3$,find the numerical value of $\frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta}$.

If $\tan \theta = \frac{1}{\sqrt{11}}$ and $0 < \theta < \frac{\pi}{2},$ then the value of $\frac{\operatorname{cosec}^{2} \theta - \sec ^{2} \theta}{\operatorname{cosec}^{2} \theta + \sec ^{2} \theta}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module