$$2cos$$θ$$+$$$$sin$$θ$$=1$$ then $$7cos$$θ$$+6sin$$θ$$=$$

Question

$$2cos$$θ$$+$$$$sin$$θ$$=1$$ then $$7cos$$θ$$+6sin$$θ$$=$$

Infinity Learn · Accepted Answer

We have $$2cos$$θ$$+$$$$sin$$θ$$=1$$⇒$$21-tan2$$θ$$21+tan2$$θ$$2+2tan$$θ$$21+tan2$$θ$$2=1$$   ∵$$cos$$θ$$=1-tan2$$θ$$21+tan2$$θ$$2$$ and $$sin$$θ$$=2tan$$θ$$21+tan2$$θ$$2$$⇒$$2-2tan2$$θ$$2+2tan$$θ$$2=1+tan2$$θ$$2$$⇒$$3tan2$$θ$$2-2tan$$θ$$2-1=0$$⇒$$tan$$θ$$2=1$$, $$tan$$θ$$2=-13$$⇒θ$$=$$π$$2$$, $$tan$$θ$$2=-13For$$ θ$$=$$π$$2$$, we have $$7cos$$θ$$+6sin$$θ$$=6For$$ $$tan$$θ$$2=-13$$, we have $$7cos$$θ$$+6sin$$θ$$=71-tan2$$θ$$21+tan2$$θ$$2+62tan$$θ$$21+tan2$$θ$$2$$                                                                      $$=71-19+12-131+19=2$$

$2 \cos θ + \sin θ = 1 then 7 \cos θ + 6 \sin θ =$

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2cosθ+sinθ=1 then 7cosθ+6sinθ=

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$2 \cos θ + \sin θ = 1 then 7 \cos θ + 6 \sin θ =$