Question
If 3sin−12x1+x2−4cos−11−x21+x2+2tan−12x1+x2=π3 then x=
Answer: Option B
:
B
3sin−12x1+x2−4cos−11−x21+x2+2tan−12x1+x2=π3
Putting x=tanθ
3sin−1(2tanθ1+tan2θ)−4cos−1(1−tan2θ1+tan2θ)
+2tan−1(2tanθ1−tan2θ)=π3
⇒3sin−1(sin2θ)−4cos−1(cos2θ)
+2tan−1(tan2θ)=π3
⇒3(2θ)−4(2θ)+2(2θ)=π3⇒6θ−8θ+4θ=π3
⇒θ=π6⇒tan−1x=π6⇒x=tanπ6=1√3
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:
B
3sin−12x1+x2−4cos−11−x21+x2+2tan−12x1+x2=π3
Putting x=tanθ
3sin−1(2tanθ1+tan2θ)−4cos−1(1−tan2θ1+tan2θ)
+2tan−1(2tanθ1−tan2θ)=π3
⇒3sin−1(sin2θ)−4cos−1(cos2θ)
+2tan−1(tan2θ)=π3
⇒3(2θ)−4(2θ)+2(2θ)=π3⇒6θ−8θ+4θ=π3
⇒θ=π6⇒tan−1x=π6⇒x=tanπ6=1√3
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