Question

if sin 2 theta=cos 3 theta then theta =?​

Answer 1

Answer:

18

when sin theta= cos theta then sum of the two theta is 90 so here 2theta +3 theta=90

5 theta=90

theta=18

hope it will help you

Answer 2

$\huge\mathfrak{Given}$

$\bf sin2 \theta = cos3 \theta$

$\huge \mathfrak{ \text{T}o \: \: Find}$

$\red{\large \mathfrak{ \text{v}alue \: of \: \bf \theta}}$

$\color{magenta}\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: \: SOLUTION \: \: \: \maltese }}}}$

$\bf sin2\theta = cos3 \theta \\ \\ \sf2sin \theta cos \theta = 4cos {}^{3} \theta - 3cos \theta \\ \\ \sf2sin \theta \: \: \cancel{cos \theta} = \cancel{cos \theta} \: \: (4cos {}^{2} \theta - 3) \\ \\ \sf 2sin \theta = 4(1 - {sin}^{2} \theta) - 3 \\ \\ \sf 2sin \theta = 4 - 4 {sin}^{2} \theta - 3 \\ \\ \large \boxed{ \boxed{ \bf{4 {sin}^{2} \theta + 2sin \theta - 1=0 }}}$

$\mathfrak{ \text{T}his \: \: is \: \: a \: \: Quadratic \: \: Eq^n \: \: in \: \: sin \theta}$

$\huge \mathcal{Now}$

$\sf sin \theta = \frac{ - 2 \pm \sqrt{4 - 4(4)( - 1)} }{8} \: \: \: \\ \mathfrak{(quadratic \: \: formula)} \\ \\ \sf sin \theta = \frac{ - 2 \pm \sqrt{4 + 16} }{8} \\ \\ \sf sin \theta = \frac{ - 2 \pm \sqrt{20} }{8} \\ \\ \green{ \large \boxed{ \boxed{ \bf sin \theta = \frac{ \sqrt{5} - 1}{4}}}}$

$\large\mathcal{HENCE} \\ \\ \huge \color{red}\boxed{ \boxed{ \mathfrak{\theta = 18 \degree}}}$

$\color{magenta}\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: \: SHORT\:\:SOLUTION \: \: \: \maltese }}}}$

We Know When SinA=CosB

then A + B =90

$\huge\mathfrak{\text{S}o,} \\ 2\theta +3 \theta =90\degree \\ \\5\theta=90\degree \\ \\ \theta=\dfrac{90}{5} \\ \\ \huge \color{red}\boxed{ \boxed{ \mathfrak{\theta = 18 \degree}}}$