Question

42. If sin 20 = cos 30 and O is an acute angle,
then sin O is equal to ​

Answer 1

${ \huge{ \bold{\underline{ \underline{ \red{Question:-:-}}}}}}$

42. If sin2θ = cos3θ and θ is an acute angle, then sinθ

is equal to

${ \huge{ \bold{\underline{ \underline{ \green{Solution:-}}}}}}$

$\star{\sf{\underline{\orange{Step\: by \: step\: explanation:-}}}}$

$\implies{\tt{\blue{sin2θ = cos3θ}}}$

$\implies{\tt{\blue{cos(90°-2θ) = cos(90°-3θ)}}}$

$\implies{\tt{\blue{90° - 2θ = 90°- 3θ}}}$

$\implies{\tt{\blue{90° = 3θ+2θ}}}$

$\implies{\tt{\blue{90° = 5θ}}}$

$\implies{\tt{\blue{ θ = \cancel\frac{90}{5}}}}$

$\implies{\tt{\blue{θ = 18°}}}$

$\leadsto\underline{\underline{\boxed{\mathtt{\color{teal}{ \theta = 18° }}}}}{\color{orange}{\bigstar}}$

Answer 2

$\huge\underline{\underline{\mathfrak{\color{teal} Given:}}}$

• $\sf{ \sin2\theta = \cos3\theta}$
• $\sf{\theta \: is \: an \: acute \: angle.}$

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{teal} To~Find:}}}$

• $\sf{The \: value \: of \: \sin\theta}$

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{teal} Solution:}}}$

$\sf{\theta \: is \: an \: acute \: angle}$

$\sf{Now,}$

$\sf{\sin2\theta = \cos3\theta}$

$\sf{\implies \sin( {90}^{0} - 2\theta) =\cos( {90}^{0} - 3\theta)}$

$\sf{\implies \cos2\theta =\cos ({90}^{0} - 3\theta) }$

$\sf{\implies 2\theta = {90}^{0} - 3\theta }$

$\sf{\implies 2\theta +3\theta = {90}^{0} }$

$\sf{\implies 5\theta = {90}^{0} }$

$\sf{\implies \theta = \cancel \frac{ {90}^{0} }{5} }$

$\sf{\implies \theta = {18}^{0} }$

$\sf\color{plum} Hence, \: the \: value \: of \: \sin\theta \: is \: {18}^{0}$

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{teal} ThankYou}}}$