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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.

    Picha ya pembetatu sahihi. Msingi ni 24, urefu haujulikani, na hypotenuse ni 25. Pembe kinyume na msingi ni kinachoitwa alpha, na angle iliyobaki ya papo hapo inaitwa beta.

    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. \(\tan ^{2} x \sin ^{3} x\)