Question

If sin 0 + cos O = √
3, then prove that
tan A+ coto= 1.
​

Answer 1

$\mathfrak{\huge{Answer:-}}\\ sinθ+cosθ= \sqrt{3} \\ Squaring \: on \: both \: the \: sides \\ {(sinθ + cosθ)}^{2} = {( \sqrt{3}) }^{2} \\ {sin}^{2} θ+ {cos}^{2}θ+2sinθcosθ=3 \\ 1+2sinθcosθ=3 \\2sinθcosθ=3-1 \\ 2sinθcosθ=2 \\ 2sinθcosθ-2=0 \\ 2(sinθcosθ-1)=0 \\ sinθcosθ-1=0 \\ sinθcosθ=1 \\ tanθ + cotθ = 1 \\ \frac{sinθ}{cosθ} + \frac{cosθ}{sinθ} = 1 \\ \frac{ {sin}^{2} θ + {cos}^{2} θ}{sinθcosθ} = 1 \\ \frac{1}{1} = 1 \\ 1 = 1\\LHS=RHS\\Hence \: proved$