Question

41. If ZA = 60°, then 3 sin? A-4 sin A =
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Answer 1

Answer:

L.H.S. = sin A sin (60 - A) sin (60 + A)

= sin A [ sin^2 60 - sin^2 A]      {sin (A + B) sin (A - B) = sin^2 A - sin^2 B }

= sin A [3/4 - sin^2 A]

= (3sin A)/4 - sin^3 A = 1/4 [3sin A - 4sin^3 A]

 =1/4sin^3 A = R.H.S.

Step-by-step explanation:

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Answer 2

${{ \bf{ \large{given}}}} \: { \rm{ \large{ \angle A = 60 \degree}}}$

${ \rm{ \large{3sinA - 4sinA}}}$

${ \rm{ \large{ = 3sin60 \degree - 4sin60 \degree}}}$

${ \rm{ \large{ = 3 \dfrac{ \sqrt{3} }{2} - 4 \dfrac{ \sqrt{3} }{2} }}}$

${ \rm{ \large{ = \dfrac{3 \sqrt{3} }{2} - \dfrac{ 4\sqrt{3} }{2} }}}$

${ \rm{ \large{ = \dfrac{3 \sqrt{3} - 4 \sqrt{3} }{2} }}}$

${ \rm{ \large{ = \dfrac{( - 1 \sqrt{3}) }{2} }}}$

${ \rm{ {So \: the \: value \: of \: 3sinA - 4sinA \: is = \dfrac{( - 1 \sqrt{3}) }{2} }}}$