Question

37. If V3 tan 0 = 1 and 0 is acute, find the values of cos 20 and si 30
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Answer 1

Answer:

Question :-

If √3 tan θ = 1 and θ is acute, find the values of con 2θ and sin 3θ

Required Answer :-

cos θ = 1/2 and sin 3θ = 1

Solution :-

$\bf \small \: √3 \: tan θ = 1$

$\bf \small \: tan θ = \frac{1}{ \sqrt{3} }$

$\bf \small \: tan \: 30 = \frac{1}{ \sqrt{3} }$

$\bf \small \: therefore \: θ \: is \: 30$

Finding cos2θ

$\bf \small \: cos2θ$

$= \bf \small \: cos2 \times 30$

$= \bf \small \:cos \: 60$

$\bf \small \: \: cos60 = \frac{1}{2}$

Finding sin 3θ

$\bf \small \: sin3θ$

$= \bf \small \: sin3 \times 30$

$= \bf \small \: sin90$

$\bf \small \: sin90 = 1$

So, cos θ = 1/2 and sin 3θ = 1