মান নির্ণয়
sinx=? \sin x= ? sinx=?
2n⋅cosx2⋅cosx22⋅⋯⋅sinx2n⋅sinx2n2^{n} \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{2^{2}} \cdot \cdots \cdot \sin \frac{x}{2^{n}} \cdot \sin \frac{x}{2^{n}}2n⋅cos2x⋅cos22x⋅⋯⋅sin2nx⋅sin2nx
2n⋅sinx2⋅cosx22⋅⋯⋅cosx2n⋅sinx2n2^{n} \cdot \sin \frac{x}{2} \cdot \cos \frac{x}{2^{2}} \cdot \cdots \cdot \cos \frac{x}{2^{n}} \cdot \sin \frac{x}{2^{n}}2n⋅sin2x⋅cos22x⋅⋯⋅cos2nx⋅sin2nx
2n⋅cosx2⋅cosx22⋅⋯⋅cosx2n⋅sinx2n2^{n} \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{2^{2}} \cdot \cdots \cdot \cos \frac{x}{2^{n}} \cdot \sin \frac{x}{2^{n}}2n⋅cos2x⋅cos22x⋅⋯⋅cos2nx⋅sin2nx
2n⋅cosx2⋅cosx22⋅⋯⋅cosx2n⋅cosx2n2^{n} \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{2^{2}} \cdot \cdots \cdot \cos \frac{x}{2^{n}} \cdot \cos \frac{x}{2^{n}}2n⋅cos2x⋅cos22x⋅⋯⋅cos2nx⋅cos2nx
Solve: sinx=sin2⋅x2=2sinx2⋅cosx2 \sin x=\sin 2 \cdot \frac{x}{2}=2 \sin \frac{x}{2} \cdot \cos \frac{x}{2} sinx=sin2⋅2x=2sin2x⋅cos2x=2cosx2⋅sin2⋅x22=2cosx2⋅2sinx22⋅cosx22 =2 \cos \frac{x}{2} \cdot \sin 2 \cdot \frac{x}{2^{2}}=2 \cos \frac{x}{2} \cdot 2 \sin \frac{x}{2^{2}} \cdot \cos \frac{x}{2^{2}} =2cos2x⋅sin2⋅22x=2cos2x⋅2sin22x⋅cos22x
=(2cosx2)⋅(2cosx22)⋅sinx22 =\left(2 \cos \frac{x}{2}\right) \cdot\left(2 \cos \frac{x}{2^{2}}\right) \cdot \sin \frac{x}{2^{2}} =(2cos2x)⋅(2cos22x)⋅sin22x
=(2cosx2)⋅(2cosx22)⋅(2cosx23)⋅sinx23=(2cosx2)⋅(2cosx22)⋅(2cosx23)⋅⋯⋯⋯(2cosx2n−1)(2cosx2n)⋅sinx2nsinx=2n⋅cosx2⋅cosx22⋅⋯⋅cosx2n⋅sinx2n \begin{array}{l} =\left(2 \cos \frac{x}{2}\right) \cdot\left(2 \cos \frac{x}{2^{2}}\right) \cdot\left(2 \cos \frac{x}{2^{3}}\right) \cdot \sin \frac{x}{2^{3}} \\ =\left(2 \cos \frac{x}{2}\right) \cdot\left(2 \cos \frac{x}{2^{2}}\right) \cdot\left(2 \cos \frac{x}{2^{3}}\right) \cdot \cdots \cdots \\ \cdots\left(2 \cos \frac{x}{2^{n-1}}\right)\left(2 \cos \frac{x}{2^{n}}\right) \cdot \sin \frac{x}{2^{n}} \\ \sin x=2^{n} \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{2^{2}} \cdot \cdots \cdot \cos \frac{x}{2^{n}} \cdot \sin \frac{x}{2^{n}} \end{array} =(2cos2x)⋅(2cos22x)⋅(2cos23x)⋅sin23x=(2cos2x)⋅(2cos22x)⋅(2cos23x)⋅⋯⋯⋯(2cos2n−1x)(2cos2nx)⋅sin2nxsinx=2n⋅cos2x⋅cos22x⋅⋯⋅cos2nx⋅sin2nx
tanθ=p হলে, cos2θ= কত? \tan \theta=p \text { হলে, } \cos 2 \theta=\text { কত? } tanθ=p হলে, cos2θ= কত?
যদি π2<θ<πএবংsinθ=35হয়, \frac{\pi}{2} < \theta < \pi এ ব ং \sin{\theta} = \frac{3}{5} হ য় , 2π<θ<πএবংsinθ=53হয়, তবে cosθ এর মান কত?
tan105∘=tan(60∘+45∘)\tan 105^{\circ}=\tan \left(60^{\circ}+45^{\circ}\right)tan105∘=tan(60∘+45∘) এর মান কত?
If cosθ=513\displaystyle \cos \theta =\frac{5}{13}cosθ=135, where θ\theta θ being an acute angle, then the value of cosθ+5cotθcosec θ−cosθ\dfrac{\cos \theta +5\cot \theta }{\text {cosec}\ \theta -\cos \theta }cosec θ−cosθcosθ+5cotθ will be
