Math  /  Trigonometry

QuestionExpress each of the following as a single trigonometric ratio. a) 2sin5xcos5x2 \sin 5 x \cos 5 x d) 2tan4x1tan24x\frac{2 \tan 4 x}{1-\tan ^{2} 4 x} b) cos2θsin2θ\cos ^{2} \theta-\sin ^{2} \theta e) 4sinθcosθ4 \sin ^{\prime} \theta \cos \theta c) 12sin23x1-2 \sin ^{2} 3 x f) 2cos2θ212 \cos ^{2} \frac{\theta}{2}-1

Studdy Solution
For expression (f) 2cos2θ21 2 \cos^2 \frac{\theta}{2} - 1 , use the identity:
2cos2A1=cos2A 2 \cos^2 A - 1 = \cos 2A
Thus,
2cos2θ21=cosθ 2 \cos^2 \frac{\theta}{2} - 1 = \cos \theta

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