Show that $\frac{\mathrm{d}}{\mathrm{d}x}\left( \tan x \right)={{\sec }^{2}}x$.[2] Show that&

Question

Show that $\frac{\mathrm{d}}{\mathrm{d}x}\left( \tan x \right)={{\sec }^{2}}x$.[2] Show that $\sin 2x\cot x=2{{\cos }^{2}}x$.[1] Hence, find the exact value of $\displaystyle\displaystyle \displaystyle\int_{\frac{\pi }{30}}^{\frac{\pi }{15}}{\cos \mathrm{ec}}\left( 10x \right)\tan \left( 5x \right)\ \mathrm{d}x$.[4]

Accepted Answer

(a) $\frac{\mathrm d}{\mathrm dx}(\tan x)=\sec^2x$ (b) $\sin2x\cot x=2\cos^2x$ (c) $\frac{\sqrt3}{15}$

2023 ASRJC P1 Q2

2023 ASRJC P1 Q2

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