Question

Tan theeta+sec theeta =1.5 find sin theeta

Answer 1

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Answer 2

Step-by-step explanation:

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

•tan A +sec A=1.5⠀⠀⠀⠀

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

⠀⠀⠀⠀ •sin A=??

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

Here,

tanA+secA=1.5

we know that,

$\bold{tanA=\dfrac{sinA}{cosA}~and ~secA=\dfrac{1}{cosA} }$ 

$\rightsquigarrow$ $\tt{\dfrac{sinA}{cosA}+\dfrac{1}{cosA}=\dfrac{15}{10} }$

$\rightsquigarrow$ $\tt{\dfrac{sinA+1}{cosA}=\dfrac{3}{2}   }$

$\rightsquigarrow$ $\tt{2×(1+sinA)=3cosA   }$

$\rightsquigarrow$ $\tt{(2(1+sinA))^2=(3cosA)^2   }$

$\bold{4(1+2sinA+sin^{2} A=9(cos^{2}A)   }$

$\bold{4sin^{2}A+8sinA+4=9(1-sin^{2}A )  }$

$\bold{4sin^{2}A+8sinA+4=9-9sin^{2}A   }$

$\bold{ 13sin^{2}A+8sinA-5=0  }$

$\bold{13sin^{2}A+13sinA-5sinA-5=0   }$

$\bold{13sinA(sinA+1)-5(sinA+1)   }$

$\bold{ (sinA+1)(13sinA-5)  }$

$\bold{sinA+1=0~or~13sinA-5=0   }$

$\bold{ sinA=-1~or~sinA=\dfrac{5}{13}  }$ 

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀⠀⠀

$\pink{ sinA=-1~or~sinA=\dfrac{5}{13}  }$