by what least integer must 4/5 be multiplied so that the product may be a positive integer? solve the sum​

by what least integer must 4/5 be multiplied so that the product may be a positive integer? solve the sum​

2 thoughts on “by what least integer must 4/5 be multiplied so that the product may be a positive integer? solve the sum​”

  1. Answer:

    sinθ+cosθ=a

    secθ+cscθ=b

    \sf\underline \red{ To\:Find}

    ToFind

    We have to find the value of b(a²-1)

    \sf\underline \pink{ Solution }

    Solution

    By putting the given values

    \begin{gathered}:\implies\sf\ \ b(a^2-1)\\ \\ \\ :\implies\sf\ \ sec\theta+csc\theta\big\{(sin\theta+cos\theta)^2-1)\big\}\\ \\ \\ \bullet\sf\ sec\theta=\dfrac{1}{cos\theta}\ \ ;\ csc\theta=\dfrac{1}{sin\theta}\\ \\ \\ :\implies\sf\ \dfrac{1}{cos\theta}+\dfrac{1}{sin\theta}\big\{sin^2\theta+cos^2\theta+2sin\theta cos\theta-1\big\}\\ \\ \\ \bullet\sf\ \ sin^2\theta+cos^2\theta=1\\ \\ \\ :\implies\sf\dfrac{sin\theta+cos\theta}{sin\theta\ cos\theta}\big\{\cancel{1}+2sin\theta\ cos\theta \cancel{-1}\big\}\\ \\ \\ :\implies\sf\ \dfrac{sin\theta+cos\theta}{\cancel{sin\theta cos\theta}}\times 2\cancel{sin\theta cos\theta}\\ \\ \\ :\implies\sf\ \ 2(sin\theta+cos\theta)\end{gathered}

    :⟹ b(a

    2

    −1)

    :⟹ secθ+cscθ{(sinθ+cosθ)

    2

    −1)}

    ∙ secθ=

    cosθ

    1

    ; cscθ=

    sinθ

    1

    :⟹

    cosθ

    1

    +

    sinθ

    1

    {sin

    2

    θ+cos

    2

    θ+2sinθcosθ−1}

    ∙ sin

    2

    θ+cos

    2

    θ=1

    :⟹

    sinθ cosθ

    sinθ+cosθ

    {

    1

    +2sinθ cosθ

    −1

    }

    :⟹

    sinθcosθ

    sinθ+cosθ

    ×2

    sinθcosθ

    :⟹ 2(sinθ+cosθ)

    \underline{\bigstar{\blue{\sf\ \ b(a^2-1)= 2(sin\theta+cos\theta)}}}

    ★ b(a

    2

    −1)=2(sinθ+cosθ

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