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  1. It is claimed that

    sin⁡ψ,cos⁡ψ,2cos⁡ψ−sin⁡ψ

    forms a geometric sequence. Prove that, if this is true, the sequence is constant, stating the constant value of the sequence.

  2. φ is chosen such that

    sin⁡φ,cos⁡φ,tan⁡φ

    forms an arithmetic sequence. Show that

    tan⁡φ=2cos⁡φ1+cos⁡φ