# v) Places A and Bare 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel

v) Places A and Bare 100 km apart on a highway. One car starts from A and another
from B at the same time. If the cars travel in the same direction at different speeds,
they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What
are the speeds of the two cars?

please solve in copy and send photo of that page​

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1. v) Places A and Bare 100 km apart on a highway. One car starts from A and another

v) Places A and Bare 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,

v) Places A and Bare 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What

v) Places A and Bare 100 km apart on a highway. One car starts from A and anotherfrom B at the same time. If the cars travel in the same direction at different speeds,they meet in 5 hours. If they travel towards each other, they meet in 1 hour. Whatare the speeds of the two cars?

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