Question

Using formula sinA=√1-cos2A/2 find the value of sin30 given that cos60=1/2​

Answer 1

Step-by-step explanation:

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Answer 2

GIVEN :–

• Value of cos(60°) = ½ .

TO FIND :–

• Value of sin(30°) = ?

SOLUTION :–

• Formula to use –

$\\ \longrightarrow { \bold{ \sin(A) = \sqrt{ \dfrac{1 - \cos(2A) }{2} } }}$

• Let's put A = 30° –

$\\ \implies { \bold{ \sin( {30}^{ \circ} ) = \sqrt{ \dfrac{1 - \cos(2 \times {30}^{ \circ} ) }{2} } }}$

$\\ \implies { \bold{ \sin( {30}^{ \circ} ) = \sqrt{ \dfrac{1 - \cos({60}^{ \circ} ) }{2} } }}$

• Put the given value –

$\\ \implies { \bold{ \sin( {30}^{ \circ} ) = \sqrt{ \dfrac{1 - \dfrac{1}{2} }{2} } }}$

$\\ \implies { \bold{ \sin( {30}^{ \circ} ) = \sqrt{ \dfrac{ \left( \dfrac{1}{2} \right) }{2} } }}$

$\\ \implies { \bold{ \sin( {30}^{ \circ} ) = \sqrt{ \dfrac{1}{4}}}}$

$\\ \implies \large { \boxed{{ \bold{ \sin( {30}^{ \circ} ) = \dfrac{1}{2} }}}}$

$\\ \rule{220}{2}$