Question

4 cos^2 a -1 =0 find the value of a​

Answer 1

Solution:

Given ,

4cos²a - 1 = 0

Simplifying

→ 4cos²a = 1

→ cos²a = 1/4

→ cos(a) = √1/4

→ cos(a) = 1/2

As we know that

cos60° = 1/2

Here ,also 1/2 = cos(a)

Substituting we have

→ cos60° = cos(a)

By comparing

→ Angle a = 60°

Hence , angle a = 60°

#LearnMore !

Some important trigonometric identities

• sin²A + cos²A = 1

• sec²A - tan²A = 1

• cosec² - tan²A = 1

• sin2A = 2sinAcosA

• sin(A + B) = sinAcosB + cosAsinB

• sin(A - B) = sinAcosB - cosAsinB

• cos2A = 2cos²A - 1

• cos(A + B) = cosAcosB - sinAsinB

• cos(A - B) = cosAcosB + sinAsinB

Answer 2

$\sf{\underline{\underline{\large{\bold{Solution}}}}}$

$\sf\longrightarrow 4 cos^2 a - 1 = 0$

$\sf\longrightarrow 4cos^2a = 1$

$\sf\longrightarrow cos^2a = \dfrac{1}{4}$

$\sf\longrightarrow cos \: a= \sqrt{\dfrac{1}{4}}$

$\sf\longrightarrow cos\:a = \dfrac{1}{2}$

$\sf{\red{\boxed{\bold{cos 60 = \dfrac{1}{2}}}}}$

$\sf\longrightarrow cos\:a = cos 60$

$\sf\longrightarrow a = 60$

____________________________

$\sf{\bold{\green{\underline{\underline{More\:about\:trignometry}}}}}$

• Trigonometry means : the science which deals with the measurements of triangles .

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \cosec & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

_______________________