All Years
1976 TYS
Question 7
Question
Show that $\frac{\mathrm{d}}{\mathrm{d}\theta} \tan^3 \theta$ may be expressed as $3\tan^4 \theta + 3\sec^2 \theta - 3.$
Hence or otherwise, find $\int_{0}^{\frac{\pi}{4}} \tan^4 \theta \ \mathrm{d} \theta.$
Show that $\frac{\mathrm{d}}{\mathrm{d}\theta} \tan^3 \theta$ may be expressed as $3\tan^4 \theta + 3\sec^2 \theta - 3.$
Hence or otherwise, find $\int_{0}^{\frac{\pi}{4}} \tan^4 \theta \ \mathrm{d} \theta.$