if sin theta plus cos theta is equal to 1/5 and 0 is less than or equal to theta less than
than tan theta is.
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We want to find the value of tanθ if sinθ+cosθ=15.
sinθ+cosθ=15⇒5sinθ+5cosθ=1.
⇒5sinθ=1−5cosθ⇒(5sinθ)2=(1−5cosθ)2.
⇒25sin2θ=1−10cosθ+25cos2θ.
⇒25−25cos2θ=1−10cosθ+25cos2θ.
⇒50cos2θ−10cosθ−24=0.
⇒(5cosθ)2−(5cosθ)−12=0.
⇒5cosθ=1±1+48√2⇒cosθ=45 or −35.
cosθ=45⇒sinθ=15−cosθ=−35.
⇒tanθ=−35×54=−34.
cosθ=−35⇒sinθ=15−cosθ=45.
⇒tanθ=45×(−53)=−43.
⇒tanθ=−34 or −43.
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