Question

if x = 30 degree then 3 sin x - 4 sin ^3 x is​

Answer 1

Given :

• x = 30°

To find :

• 3 sin x - 4( sin³ x)

Solution :

To find the value of 3 sin x - 4( sin³ x) we will put x = 30° :-

⟹ 3 sin x - 4( sin³ x)

⟹ 3 sin 30° - 4( sin³ 30°)

we know that :- sin 30° = 1/2

⟹( 3× 1/2 )- 4( 1/2)³

⟹( 3/2 )-[ 4( 1/2) × (1/2) ×( 1/2)]

⟹( 3/2 )- ( 1/2)

⟹( 3-1) / 2

⟹ 2/ 2

⟹ 1

Answer : 1

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Learn more :-

• Sin 30° = 1/2

• cos 30° = √3/2

• tan 30° = 1/√3

• Sin 45° = 1/√2

• cos 45° = 1/√2

• tan 45° = 1

• Sin 60° = √3/2

• cos 60° = 1/2

• tan 60° = √3

• Sin 90° = 1

• cos 90° = 0

• tan 90° = infinite

• cosec x = 1/ sin x

• sec x = 1/ cosx

• cot x = 1/tan x

• sin²x + cos²x = 1

• 1 + tan²x= sec²x

• cosec²x - cotx = 1

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Answer 2

GIVEN :-

• x = 30°.

TO FIND :-

• The Value of 3 sinx - 4 sin³x.

SOLUTION :-

$\begin{gathered}\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}\end{gathered}$

Put value of x in the equation 3 sinx - 4 sin³x.

$\\ \\ : \implies \displaystyle \sf \: 3 \sin30 ^ {\circ} - 4 \sin ^{3} 30 ^{ \circ}$

$\because\displaystyle \sf \: \sin30 ^ {\circ} = \dfrac{1}{2}$

$: \implies \displaystyle \sf 3 \times \frac{1}{2} - 4 \times \bigg( \frac{1}{2} \bigg) ^{ 3}$

$: \implies \displaystyle \sf \dfrac{3}{2} - 4 \times \dfrac{1}{8}$

$: \implies \displaystyle \sf \dfrac{3}{2} - \dfrac{4}{8}$

$: \implies \displaystyle \sf \frac{12 - 4}{8}$

$: \implies \displaystyle \sf \cancel \dfrac{8}{8}$

$: \implies \displaystyle \sf \underline{ \boxed{3 \sin30 ^ {\circ} - 4 \sin ^{3} 30 ^{ \circ} = 1}}$

$\therefore\underline {\displaystyle \sf value \: of \: 3 \sin30 ^ {\circ} - 4 \sin ^{3} 30 ^{ \circ} \: is \: 1}$