# Ch 10: Trigonometric Identities

• 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)
• fsc-part1-ptb/important-questions/ch10-trigonometric-identities