Question

If sin θ = √3 cos θ, 0° < θ < 90°, then θ is equal to

Answer 1

Step-by-step explanation:

$\huge\star\bold\red{ANSWER}$

sinθ+cosθ= 3

SQUARING BOTH SIDE....

=>(sinθ+cosθ)²= 3

=>sin2θ+cos 2θ+2sinθcosθ=3

⇒2sinθcosθ=2

⇒sinθcosθ=1

⇒sinθcosθ=sin²θ+cos²θ

⇒1=(sin²θ+cos²θ)/(sinθ×cosθ)

⇒tanθ+cotθ=1

Answer 2

$\huge\sf\pink{Answer}$

☞ Your Answer is 60°

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$\huge\sf\blue{Given}$

✭ sin θ = √3 cos θ

✭ θ is acute , that is 0°< θ<90°

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$\huge\sf\gray{To \:Find}$

◈ The Value of θ?

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$\huge\sf\purple{Steps}$

$\bullet\underline{\textsf{As Per the Question}}$

$\sf{\dashrightarrow sin\theta=\sqrt{3}cos\theta}$

$\sf{\dashrightarrow\dfrac{\sin\theta}{cos\theta}=\sqrt{3}}$

$\sf{\dashrightarrow\tan\theta=\sqrt{3}}$

$\sf{\dashrightarrow tan\theta=tan60^{\circ}}$

$\textsf{Eliminating tan both sides}$

$\orange{\sf{\dashrightarrow \theta=60^{\circ}}}$

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$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$

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