মান নির্ণয়
3cosx−sinx=23 \sqrt{3} \cos x-\sin x=\frac{2}{3} 3cosx−sinx=32 হলে , sin3x= \sin 3 x= sin3x=
−2327-\frac{23}{27} −2723
123\frac{1}{23} 231
2327\frac{23}{27} 2723
2325\frac{23}{25} 2523
Solve: 3cosx−sinx=23 \sqrt{3} \cos x-\sin x=\frac{2}{3} 3cosx−sinx=32
⇒32cosx−12sinx=13⇒cosxcos30∘−sinxsin30∘=13⇒cos(x+30∘)=13 এখন, cos{3(x+30∘)}=cos(90∘+3x)⇒4cos3(x+30∘)−3cos(x+30∘)⇒4(13)3−3×13=−sin3x=−sin3x⇒sin3x=1−427=2327 \begin{aligned} \Rightarrow & \frac{\sqrt{3}}{2} \cos x-\frac{1}{2} \sin x=\frac{1}{3} \\ \Rightarrow & \cos x \cos 30^{\circ}-\sin x \sin 30^{\circ}=\frac{1}{3} \\ \Rightarrow & \cos \left(x+30^{\circ}\right)=\frac{1}{3} \\ & \text { এখন, } \cos \left\{3\left(x+30^{\circ}\right)\right\}=\cos \left(90^{\circ}+3 x\right) \\ \Rightarrow & 4 \cos ^{3}\left(x+30^{\circ}\right)-3 \cos \left(x+30^{\circ}\right) \\ \Rightarrow & 4\left(\frac{1}{3}\right)^{3}-3 \times \frac{1}{3}=-\sin 3 x \quad=-\sin 3 x \\ \Rightarrow & \sin 3 x=1-\frac{4}{27}=\frac{23}{27} \end{aligned} ⇒⇒⇒⇒⇒⇒23cosx−21sinx=31cosxcos30∘−sinxsin30∘=31cos(x+30∘)=31 এখন, cos{3(x+30∘)}=cos(90∘+3x)4cos3(x+30∘)−3cos(x+30∘)4(31)3−3×31=−sin3x=−sin3xsin3x=1−274=2723
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
