Question

★ Question :-

If tan30° sin60° = tan60° cos60° tanA, then A = _____ degrees.

(a) 0

(b) 30

(c) 45

(d) 60

↦Explanation needed!!

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Answer 1

Answer:

b) 30

Step-by-step explanation:

Answer 2

❍ Given :-

• tan30° sin60° = tan60° cos60° tanA

❍ To Find :-

• The value of A

❍ Solution :-

$→ \mathtt {\small \tan30° \sin60° = \tan60° \cos60° \tan A}$

$→ \mathtt{\frac{1}{\cancel{\sqrt{3}}} \times \frac{\cancel{\sqrt{3}}}{2} = \sqrt{3} \times \frac{1}{2} \times \tan A}$

$\mathtt{→ \frac{1}{2} = \frac{\sqrt{3}}{2} \times \tan A}$

$\mathtt{→ \tan A = \frac{1}{\cancel{2}} \times \frac{\cancel{2}}{\sqrt{3}}}$

$\mathtt{→ \tan A = \frac{1}{\sqrt{3}}}$

We know that tan 30° = $\frac{1}{\sqrt{3}}$ .

Therefore, A = 30°.

Trigonometric Ratios:-

$\begin{gathered}\begin{array}{ | c|c|c|c|c|c |}\hline \rm\angle\:A& \: \: \: 0\degree&30\degree&45\degree&60\degree&90\degree\\ \hline \rm\sin \: A&0& \dfrac{ 1}{2}&\dfrac{1}{\sqrt{2}}&\dfrac{\sqrt{3}}{2}&1\\ \hline \rm\cos \:A&1& \dfrac{ \sqrt{3} }{2} & \dfrac{1}{ \sqrt{2}} & \dfrac{1}{2}&0 \\ \hline \rm \tan \: A&0& \dfrac{1}{ \sqrt{3} }&1& \sqrt{3}& \rm{ \infty } \\ \hline \rm\cosec \: A& \infty & 2& \sqrt{2} & \dfrac{2}{\sqrt{3} }&1 \\ \hline \rm\sec \: A&1& \dfrac{2}{ \sqrt{3} }& \sqrt{2}&2 & \infty \\ \hline \rm \cot \: A& \infty & \sqrt{3} &1& \dfrac{1}{ \sqrt{3} }&0 \\ \hline \end{array}\end{gathered}$