cos(thita)[sin(thita)+root sin(square)((thita)+sin(square)(alpha)]always lies between the values (plus minus)root 1+sin(square)alpha

Dear ravi

cosθ[sinθ + √{sin²θ +sin²α}]

[cosθ]sinθ + cosθ [√{sin²θ +sin²α}]

we know that     asinθ + bcosθ   lies between    - √{a² +b²}  to  √{a² +b²}

so  given expression lies between   -√{cos²θ + sin²θ +sin²α}  to √{cos²θ + sin²θ +sin²α}

   or                                           -  √{1 +sin²α}   to    √{1 +sin²α}

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