Math, asked by Anonymous, 5 months ago

Choose the correct answer from the following alternatives.

2 tan 30

1+ tan 30

(A) cos 60

(B) sin 60 (C) tan 60° (D) cot​

Answers

Answered by pulakmath007
2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Choose the correct answer from the following alternatives.

 \displaystyle \sf{ \frac{2 \tan  {30}^{ \circ} }{1 +  { \tan}^{2}  {30}^{ \circ} } }

(A) cos 60°

(B) sin 60°

(C) tan 60°

(D) cot 60°

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric formula that

 \displaystyle \sf{  \sin 2 \theta = \frac{2 \tan \theta  }{1 +  { \tan}^{2}  \theta } }

EVALUATION

 \displaystyle \sf{  \sin 2 \theta = \frac{2 \tan \theta  }{1 +  { \tan}^{2}  \theta } }

Putting θ = 30° we get

 \displaystyle \sf{  \sin (2  \times  {30}^{ \circ} )= \frac{2 \tan {30}^{ \circ}   }{1 +  { \tan}^{2}  {30}^{ \circ} } }

 \displaystyle \sf{  \implies \sin   {60}^{ \circ} = \frac{2 \tan {30}^{ \circ}   }{1 +  { \tan}^{2}  {30}^{ \circ} } }

FINAL ANSWER

Hence the correct option is (B) sin 60°

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