If fx-sin x -sin 2 x -sin 3 x- then which of the following is-are true

F(x)=sin x ·sin 2 x ·sin 3 x =12sin 2 x(2 sin 3 x sin x) =12sin 2 x(cos 2 x cos 4 x) =14(2 sin 2 x cos 2 x 2 cos 4 x sin 2 x) f(x)=14(sin 4 x sin 6 x+sin 2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Differentiation Using Substitution

If fx=sin x ·...

Question

If $f (x) = sin x \cdot sin 2 x \cdot sin 3 x$ , then which of the following is/are true

f^{'} (\frac{π}{2}) = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f^{'} (\frac{π}{2}) = 2

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

f^{''} (\frac{π}{12}) = \frac{17 - 4 \sqrt{3}}{2}

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

f^{''} (\frac{π}{12}) = \frac{13}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $f^{''} (\frac{π}{12}) = \frac{17 - 4 \sqrt{3}}{2}$
$f (x) = sin x \cdot sin 2 x \cdot sin 3 x = \frac{1}{2} sin 2 x (2 sin 3 x sin x) = \frac{1}{2} sin 2 x (cos 2 x - cos 4 x) = \frac{1}{4} (2 sin 2 x cos 2 x - 2 cos 4 x sin 2 x) f (x) = \frac{1}{4} (sin 4 x - sin 6 x + sin 2 x) \Rightarrow f^{'} (x) = \frac{1}{4} (2 cos 2 x + 4 cos 4 x - 6 cos 6 x) \Rightarrow f^{''} (x) = \frac{1}{4} (- 4 sin 2 x - 16 sin 4 x + 36 sin 6 x) ∴ f^{''} (x) = 9 sin 6 x - 4 sin 4 x - sin 2 x$

So,
$f^{'} (\frac{π}{2}) = 2 f^{''} (\frac{π}{12}) = \frac{17 - 4 \sqrt{3}}{2}$

Suggest Corrections

Similar questions

Q. If

\int \sqrt{1 + sin x} \cdot f (x) d x = \frac{2}{3} {(1 + sin x)}^{3 / 2} + C

, then

f (x)

is equal to

Q. If

y = \sqrt{[sin x + \sqrt{sin x + \sqrt{sin x + \sqrt{(sin x + \cdot \cdot \cdot \infty)}}}]}

, then

Q. If

{cos}^{3} x sin 2 x = a_{1} sin x + a_{2} sin 2 x + \dots + a_{n} sin n x

\forall x \in R

, where

a_{n} \neq 0

, then which of the following is/are correct ?

Q. Let

0 \leq x, y, z \leq \frac{π}{2}

such that

sin x \cdot sin y \cdot cos z = \frac{1}{4 \sqrt{2}}, \frac{{sin}^{2} x \cdot {sin}^{3} y}{cos z} = \frac{1}{4 \sqrt{2}} and \frac{sin x \cdot {sin}^{4} y}{{cos}^{2} z} = \frac{1}{8}

, then which of the following is/are correct?

Q. cos4x cos 3x + cos2.x21.sin 4x + sin 3x +sin 2x=cot 3x,r + sin 2x

Join BYJU'S Learning Program

Explore more

Differentiation Using Substitution

Standard XII Mathematics

Join BYJU'S Learning Program

If f(x)=sinx⋅sin2x⋅sin3x, then which of the following is/are true

If $f (x) = sin x \cdot sin 2 x \cdot sin 3 x$ , then which of the following is/are true