# Ch 09: Fundamental of Trigonometry

• Find the value of the remaining trigonometric functions of $\theta$, If $cos \theta=\frac{12}{13}$ and the terminal side of the angle is not in the $I$ Quadrant. — BISE Gujrawala(2015)
• Express in radian $120'40''$ — BISE Gujrawala(2017)
• Verify $2$ $sin 45^{\circ} +\frac{1}{2}cos 45^{\circ}=\frac{3}{\sqrt{2}}$ — BISE Gujrawala(2017), BISE Sargodha(2017)
• Prove that $cosce \theta+tan\theta sec \theta=cosec \theta sec^2 \theta$ — BISE Gujrawala(2017)
• Prove that $(tan\theta+cot\theta)^2=sec^2\theta cosec^2\theta$ — BISE Gujrawala(2017)
• Convert $150^{\circ}$ into radian. — BISE Sargodha(2015)
• Find $\theta$ when $l=1.5cm$, $r=2.5cm$ — BISE Sargodha(2015)
• Prove that $\frac{cos\theta+sin\theta}{cos\theta-sin\theta}+\frac{cos\theta-sin\theta}{cos\theta+sin\theta}$ — BISE Sargodha(2015)
• Find $l$ when $\theta=65^{\circ}20'$, $r=18mm$ — BISE Sargodha(2015), BISE Lahore(2017)
• Find the value of remaining trigonometric functions if $tan\theta=-\frac{1}{3}$ and the terminal arm of the angle in $II$-Quad. — BISE Sargodha(2016)
• Prove that $(sec\theta-tan\theta)^2=\frac{1-sin\theta}{1+sin\theta}$ — BISE Sargodha(2016)
• If $cosec\theta =\frac{m^2+1}{2m}$ and $m>0$, $(0<\theta<\frac{\pi}{2})$, find the values of the remaining trigonometric ratios. — BISE Sargodha(2016)
• Convert that $\frac{1}{1+sin\theta}+\frac{1}{1-sin\theta}=2sec^2\theta$ — BISE Sargodha(2017)
• Prove that $\frac{sin\theta}{1+cos\theta}+cot\theta=cosec\theta$ — BISE Lahore(2017)
• If $tan^245^{\circ}-cos^260^{\circ}=xsin45^{\circ}cos45^{\circ}tan60^{\circ}$ then find $x$ — BISE Lahore(2017)
• $\frac{tan\theta+sec\theta-1}{tan\theta-sec\theta+1}=tan\theta+sec\theta$ — FBISE(2016), FBISE(2017)
• Express the sexagasimal measure $75^{\circ}6'30''$ into the measurement. — FBISE(2016)