====== Ch 10: Trigonometric Identities ======
<list-group>
  * Prove that (without calculator) $\sin 10^{\circ}\sin 30^{\circ}\sin 50^{\circ}\sin 70^{\circ}=\frac{1}{16}$ --- // BISE Gujrawala(2015)//
  * Prove that $\sin(\frac{\pi}{4}-\theta)\sin(\frac{\pi}{4}+\theta)=\frac{1}{2}\csc^2\theta$ --- // BISE Gujrawala(2017)//
  * Prove that $\sin(\theta+\frac{\pi}{6})=\cos\theta$ --- // BISE Gujrawala(2017)//
  * Using without table or calculator find $tan(1110^{\circ})$ --- // BISE Sargodha(2015), BISE Gujrawala(2017)//
  * Prove that $sin(180^{\circ}+\alpha)sin(90^{\circ}-\alpha)=-sin\alpha cos\alpha$ --- // BISE Sargodha(2015), BISE Lahore(2017)//
  * Prove that (without calculator) $sin\frac{\pi}{9}sin\frac{2\pi}{9}sin\frac{\pi}{3}sin\frac{4\pi}{9}=\frac{3}{16}$  --- // BISE Sargodha(2015)//
  * Prove that $cot\alpha-tan\alpha=2cot2\alpha$ --- // BISE Sargodha(2015)//
  * Find the value of $cos15^{circ}$ using without table or calculator.--- // BISE Sargodha(2015)//
  * If $\alpha$, $\beta$, $\gamma$ are the angles of $\triangle ABC$, show that $cot\frac{\alpha}{2}+cot\frac{\beta}{2}+cot\frac{\gamma}{2}=cot\frac{\alpha}{2}cot\frac{\beta}{2}cot\frac{\gamma}{2}$ --- // BISE Sargodha(2015)//
  * If $\alpha$, $\beta$, $\gamma$ are the angles of triangle $ABC$, prove that $cos20^{\circ}cos40^{\circ}cos80^{\circ}=\frac{1}{8}$ --- // BISE Sargodha(2016)//
  * Find the value of $cos\frac{\pi}{12}$ --- // BISE Sargodha(2017)//
  * Show that $\frac{cose\theta+2cosec2\theta}{sec\theta}=cot\frac{\theta}{2}$ --- // BISE Sargodha(2017)//
  * Prove that $\frac{cos3\theta}{cos\theta}+\frac{sin3\theta}{sin\theta}=4cos2\theta$ --- // BISE Sargodha(2017)//
  * Prove that $sin(45^{\circ}+\alpha)=\frac{1}{\sqrt{2}}(sin\alpha+cos\alpha)$ --- // BISE Lahore(2017)//
  * Prove that $\frac{sin\theta+sin3\theta+sin5\theta+sin7\theta}{cos\theta+cos3\theta+cos5\theta+cos7\theta}=tan4\theta$--- // BISE Lahore(2017)//
  * Prove that $\frac{cos8^{\circ}-sin8^{\circ}}{cos8^{\circ}+sin8^{\circ}}=tan37^{\circ}$ --- // FBISE (2016)//
  * Using without table or calculator, prove that $sin19 cos11+sin71 sin11=\frac{1}{2}$ --- // FBISE (2017)//
  * Prove that $sin\frac{\pi}{9}sin\frac{2\pi}{9}sin\frac{\pi}{3}sin\frac{4\pi}{9}=\frac{3}{16}$--- // FBISE (2017)//
  * Prove that $cos330 sin600+cos120 sin150=-1$  --- // BISE Gujrawala(2015)//




</list-group>
{{tag>FSc FSc_Part1 Important_Questions_FSc_1}}