Which of the following pair of functions are identical?

\sqrt{1 + sin x}, sin \frac{x}{2} + cos \frac{x}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x, \frac{x^{2}}{x}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{x^{2}}, {(\sqrt{x})}^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

l n x^{3} + l n x^{2}, 5 l n x

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
A $\sqrt{1 + sin x}, sin \frac{x}{2} + cos \frac{x}{2}$
B $x, \frac{x^{2}}{x}$
C $\sqrt{x^{2}}, {(\sqrt{x})}^{2}$
D $l n x^{3} + l n x^{2}, 5 l n x$

Suggest Corrections

Similar questions

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^{2} | x |$ (b) f(x) = $e^{x} + e^{- x}$

(e) f(x) = log(x + $\sqrt{x^{2} + 1}$ (f) $a^{x} - a^{- x}$

(g) f(x) = $sin x + cos x$ (h) $sin x \times (e^{x} - e^{- x})$

{(sin x + csc x)}^{2} + {(cos x + sec x)}^{2} = {tan}^{2} x + {cot}^{2} x + 7

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^{2} | x |$ (b) f(x) = $e^{x} + e^{- x}$

(e) f(x) = log(x + $\sqrt{x^{2} + 1}$ (f) $a^{x} - a^{- x}$

(g) f(x) = $sin x + cos x$ (h) $sin x \times (e^{x} - e^{- x})$

y = s i n (x) + l n (x^{2}) + e^{2 x}

d y / d x

You are given $c o s x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .;$

$s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$

$t a n x = x + \frac{x^{3}}{3} + \frac{2. x^{5}}{15} . . . . . .$

Find the value of $lim x \to 0 \frac{x c o s x + s i n x}{x^{2} + t a n x}$

Join BYJU'S Learning Program