The most general value of - satisfying both the equations sin - - 1-2- tan - - 1-3 is n - Z

The correct option is A sin θ = 1/2⇒ sin θ = sin ( π/6 ) ⇒θ = n π + ( 1)^n ( π/6 ) tan θ = 1/√(3)⇒ tan θ = tan ( π/6 )⇒θ = n π + ( π/6 ) Common solution ...

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Byju's Answer

Standard XI

Mathematics

Solving Simultaneous Trigonometric Equations

The most gene...

Question

The most general value of $θ$ satisfying both the equations $s i n θ = \frac{1}{2}, t a n θ = \frac{1}{\sqrt{3}} i s (n ϵ Z)$

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Solution

The correct option is A
$s i n θ = \frac{1}{2} \Rightarrow s i n θ = s i n (\frac{π}{6}) \Rightarrow θ = n π + (- 1)^{n} (\frac{π}{6}) t a n θ = \frac{1}{\sqrt{3}} \Rightarrow t a n θ = t a n (\frac{π}{6}) \Rightarrow θ = n π + (\frac{π}{6}) C o m m o n s o l u t i o n o f θ i s 2 n π + (\frac{π}{6}) . n ϵ Z .$

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The most general value of θ satisfying both the equations sinθ=12,tanθ=1√3is(nϵZ)

The correct option is A sinθ=12⇒sinθ=sin(π6)⇒θ=nπ+(−1)n(π6)tanθ=1√3⇒tanθ=tan(π6)⇒θ=nπ+(π6)Common solution of θ is 2 nπ+(π6).nϵZ.

The most general value of $θ$ satisfying both the equations $s i n θ = \frac{1}{2}, t a n θ = \frac{1}{\sqrt{3}} i s (n ϵ Z)$