Question

(if theta= 30°)
cos3 theta = 4cos^3 theta - 3 cos theta​

Answer 1

Question:-

If θ= 30° then ,Prove that cos 3×θ = 4cos³θ - 3 cos θ

Solution:-

Given θ=30⁰

We have

⇒cos 3× θ = 4cos³θ - 3 cos θ

⇒cos 3×30⁰ = 4cos³30⁰ - 3 cos 30⁰

⇒cos 90⁰ = 4cos³30⁰ - 3 cos 30⁰

Putting the value of cos 30⁰=√3/2 and cos 90⁰=0

$\implies \sf \: 0= 4 \times \bigg( \dfrac{ \sqrt{3} }{ \: 2} \bigg) ^{3} - 3 \times \bigg( \dfrac{ \sqrt{3} }{ \: 2} \bigg)$

$\implies \sf \:0= 4 \times \bigg( \dfrac{ 3\sqrt{3} }{ \: 8} \bigg) - \bigg( \dfrac{ 3\sqrt{3} }{ \: 2} \bigg)$

$\implies \sf \:0= \cancel{\bigg( \dfrac{ 3\sqrt{3} }{ \: 2} \bigg) }-\cancel{\bigg( \dfrac{ 3\sqrt{3} }{ \: 2} \bigg) }$

$\implies \sf0 = 0$

$\large \implies \sf LHS=RHS$

Hence, proved

$\sf$

More to know

➠sin 0⁰ =0

➠sin 30⁰=1/2

➠sin 45⁰=1/√2

➠sin 60⁰=√3/2

➠sin 90⁰= 1

---------------------------------

➠cos 0⁰ =1

➠cos 30⁰=√3/2

➠cos 45⁰=1/√2

➠cos 60⁰=1/2

➠cos 90⁰= 0

---------------------------------

➠tan 0⁰ =0

➠tan 30⁰=1/√3

➠tan 45⁰=1

➠tan 60⁰=√3

➠tan 90⁰= not defined

---------------------------------

➠cosec 0⁰ =not defined

➠cosec 30⁰=2

➠cosec 45⁰=√2

➠cosec 60⁰=2/√3

➠cosec 90⁰= 1

----------------------------------

➠sec 0⁰ =1

➠sec 30⁰=2/√3

➠sec 45⁰=√2

➠sec 60⁰=2

➠sec 90⁰= not defined

-----------------------------------

➠cot 0⁰ =not defined

➠cot 30⁰=√3

➠cot 45⁰=1

➠cot 60⁰=1/√3

➠cot 90⁰= 0

------------------------------------