9.3E: Mbili-Angle, Nusu-Angle, na Kupunguza Formula (Mazoezi)
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Kwa mazoezi yafuatayo, pata thamani halisi.
20. Pata\(\sin (2 \theta), \cos (2 \theta),\)\(\cos \theta=-\frac{1}{3}\) na\(\tan (2 \theta)\) kupewa na\(\theta\) iko katika kipindi\(\left[\frac{\pi}{2}, \pi\right]\).
21. Kupata\(\sin (2 \theta), \cos (2 \theta),\) na\(\tan (2 \theta)\) kupewa sec\(\theta=-\frac{5}{3}\) na\(\theta\) ni katika kipindi\(\left[\frac{\pi}{2}, \pi\right]\).
22. \(\sin \left(\frac{7 \pi}{8}\right)\)
23. \(\sec \left(\frac{3 \pi}{8}\right)\)
Kwa mazoezi yafuatayo, tumia Kielelezo 1 ili kupata kiasi kilichohitajika.
Kielelezo 1
24. \(\sin (2 \beta), \cos (2 \beta), \tan (2 \beta), \sin (2 \alpha), \cos (2 \alpha),\)na\(\tan (2 \alpha)\)
25. \(\sin \left(\frac{\beta}{2}\right), \cos \left(\frac{\beta}{2}\right), \tan \left(\frac{\beta}{2}\right), \sin \left(\frac{\alpha}{2}\right), \cos \left(\frac{\alpha}{2}\right),\)na\(\tan \left(\frac{\alpha}{2}\right)\)
Kwa mazoezi yafuatayo, kuthibitisha utambulisho.
26. \(\frac{2 \cos (2 x)}{\sin (2 x)}=\cot x-\tan x\)
27. \(\cot x \cos (2 x)=-\sin (2 x)+\cot x\)
Kwa mazoezi yafuatayo, fungua upya maneno bila mamlaka.
28. \(\cos ^{2} x \sin ^{4}(2 x)\)
29. \(\tan ^{2} x \sin ^{3} x\)