HPC WB3.7 - Trig Proofs Day 2
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Last updated about 5 years ago
8 questions
1
Verify \frac{1-\cos 2x}{\cos^2 x} = 2\tan^2 x.
Verify \frac{1-\cos 2x}{\cos^2 x} = 2\tan^2 x.
1
Verify 2\tan 2x\cos 2x = \frac{\sin 4x}{\cos 2x}.
Verify 2\tan 2x\cos 2x = \frac{\sin 4x}{\cos 2x}.
1
Verify 2\cos^2 x \sin x = \frac{\sin 2x}{\sec x}.
Verify 2\cos^2 x \sin x = \frac{\sin 2x}{\sec x}.
1
Verify 2\sin x \cos x + \sec^{2} x = 1+ \sin 2x+ \tan^2 x.
Verify 2\sin x \cos x + \sec^{2} x = 1+ \sin 2x+ \tan^2 x.
1
Verify \tan\left( \frac{\pi}{4} + \theta \right) = \frac{1+\tan \theta}{1-\tan \theta}.
Verify \tan\left( \frac{\pi}{4} + \theta \right) = \frac{1+\tan \theta}{1-\tan \theta}.
1
Verify \tan\left( \theta - 135^\circ \right) = \frac{\tan \theta +1}{1-\tan \theta}.
Verify \tan\left( \theta - 135^\circ \right) = \frac{\tan \theta +1}{1-\tan \theta}.
1
Verify \tan\left(\frac{3\pi}{4}+\theta\right) = \frac{\tan\theta -1}{\tan\theta +1}.
Verify \tan\left(\frac{3\pi}{4}+\theta\right) = \frac{\tan\theta -1}{\tan\theta +1}.
1
Verify \frac{\cot^2 x - 2\cos^2 x}{\cot x} = \frac{\cos 2x}{\tan x}.
Verify \frac{\cot^2 x - 2\cos^2 x}{\cot x} = \frac{\cos 2x}{\tan x}.